Simplification of Switching Function Free Essays

EEN1036 Digital Logic Design Chapter 4 part I Simplification of Switching Function 1 Objective s s s s Simplifying logic circuit Minimization using Karnaugh map Using Karnaugh map to obtain simplified SOP and POS expression Five-variable Karnaugh map 2 Simplifying Logic Circuits †¢ †¢ †¢ A A Boolean expression for a logic circuit may be reduced to a simpler form The simplified expression can then be used to implement a circuit equivalent to the original circuit Consider the following example: B C A B C + A BC Y AB C + AB C Y = A B C + A BC + AB C + AB C 3 Continue †¦ Checking for common factor: Y = A B C + A BC + AB C + AB C = A C ( B + B ) + AB (C + C ) Reduce the complement pairs to ‘1’ Y = A C ( B + B ) + AB (C + C ) = A C + AB Draw the circuit based on the simplified expression A B C Y 4 Continue †¦ †¢ A Consider another logic circuit: B C Y Y = C( A + B + C ) + A + C Convert to SOP expression: Y = C( A + B + C ) + A + C = AC + B C + AC Checking for common factor: Y = A(C + C ) + B C = A + BC 5 Continue †¦ †¢ †¢ Simplification of logic circuit algebraically is not always an easy task The following two steps might be useful: i. The original expression is convert into the SOP form by repeated application of DeMorgan’s theorems and multiplication of terms ii. The product terms are then checked for common factors, and factoring is performed wherever possible 6 Continue †¦ †¢ Consider the truth table below: A 0 0 0 0 1 B 0 0 1 1 0 C 0 1 0 1 0 Y 0 0 1 0 0 Minterm Boolean expression: Simplify to yield: Y = A BC + ABC + AB C Y = BC ( A + A) + AB C = BC + AB C 1 0 1 1 1 1 0 1 1 1 1 0 †¢ If minterms are only differed by one bit, they can be simplified, e. We will write a custom essay sample on Simplification of Switching Function or any similar topic only for you Order Now g. A BC ABC 7 Continue †¦ †¢ More example: A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 Y 0 1 1 0 0 1 1 0 Minterm Boolean expression: Y = A B C + A BC + AB C + ABC Minterms 1 and 5, 2 and 6 are only differ by one bit: Y = B C ( A + A) + BC ( A + A) = BC + B C A B C Y 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 Minterm Boolean expression: Y = A B C + A BC + AB C + ABC Checking and factoring minterms differed by only by one bit: Y = A C ( B + B ) + AC ( B + B ) = A C + AC = C ( A + A) =C 8 Continue †¦ †¢ †¢ †¢ Though truth table can help us to detect minterms which are only differed by one bit, it is not arranged in a proper way A Karnaugh map (K-map) is a tool, which help us to detect and simplify minterms graphically It is a rearrangement of the truth table where each adjacent cell is only differed by one bit By looping adjacent minterms, it is similar to grouping the minterms with a single bit difference on the truth table 9 K arnaugh Map †¢ †¢ A K-map is just a rearrangement of truth table, so that minterms with a single-bit difference can be detected easily Figure below shows 4 possible arrangement of 3-variable K-map A BC 0 0 01 1 11 3 10 2 C AB 00 0 01 2 11 6 10 4 0 1 4 5 7 6 0 1 1 3 7 5 AB C 0 0 1 1 BC A 0 0 1 4 00 01 2 3 00 01 1 5 11 6 7 11 3 7 10 4 5 10 2 6 10 Continue †¦ †¢ Figure below show two possible arrangement of 4variable K-map CD AB 00 0 01 1 11 3 10 2 AB 00 CD 01 4 11 12 10 8 00 01 4 5 7 6 00 0 01 1 5 13 9 11 12 13 15 14 11 3 7 15 11 10 8 9 11 10 10 2 6 14 10 †¢ Notice that the K-map is labeled so that horizontally and vertically adjacent cells differ only by one bit. 11 Continue †¦ †¢ The K-map for both SOP and POS form are shown below: C D C D CD C D AB AB AB 0 1 3 2 C+D C+ D C + D C +D A +B 0 1 3 2 4 5 7 6 A+B A+B A +B 4 5 7 6 12 13 15 14 12 13 15 14 AB 8 9 11 10 8 9 11 10 SOP form (minterm) POS form (maxterm) †¢ †¢ The simplified SOP expression can be obtained by properly combining those adjacent cells which contains ‘1’ This process of combining adjacent minterms is known as 12 looping Continue †¦ †¢ †¢ Each loop of minterms will form a group which can be represented by a product term When a variable appears in both complemented and uncomplemented form within a group, that variable is eliminated from the product term C D C D CD C D AB AB AB AB 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 group 2 group 1: C D( AB + AB ) = AC D group 2: AB(C D + CD ) = ABD Simplified SOP expression: Y = AC D + ABD 13 group 1 Continue †¦ †¢ Consider another K-map: C D C D CD C D AB AB AB AB 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 group 1 C D C D CD C D AB AB AB AB 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 14 group 1: ( A B + AB )(C D + CD ) = BD Simplified SOP expression: Y = BD group 1: C D ( A B + A B + AB + AB ) = C D Simplified SOP expression: Y = CD group 1 From truth table to K-map †¢ The content of each cell can be directly plot on the Kmap according to the truth table Consider the following example: 0 1 2 3 4 5 6 7 A 0 0 0 0 1 1 1 1 B C Y 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 B C B C BC B C A A 1 0 1 1 0 3 1 2 0 4 0 5 0 7 1 6 AB BC Simplified SOP expression: Y = A B + BC 15 Continue †¦ †¢ Consider the following 4-variable K-map A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C D Y 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 C D C D CD C D AB AB AB 0 0 0 1 1 1 0 1 0 0 1 0 3 0 0 0 ACD 2 4 5 7 6 12 13 15 14 AB 0 8 9 11 0 10 ABD Simplified SOP expression: Y = A C D + ABD 16 Continue †¦ †¢ Some guidelines: i. Construct K-map and fill it according to the truth table ii. Only loop cells in the power of 2, i. e. 2 cells, 4 cells, 8 cells and so on iii. Always start by looping the isolated minterms iv. Look for minterms which are adjacent to only one minterm and loop them together v. Proceed on to loop the largest possible groups, from eight minterms (octet), 4 minterms (quad) to 2 minterms (pair) vi. Obtain the product term for each group vii. The sum of these product terms will be the simplified SOP expression 17 Continue †¦ Example: a. Obtain the simplify SOP expression for the truth table: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Y 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 C D C D CD C D AB AB AB AB A B CD 0 0 0 0 0 0 1 1 0 1 0 1 1 3 1 0 0 0 2 4 5 7 6 12 13 15 14 8 9 1 11 10 BD ACD Simplified SOP expression: Y = A B CD + ACD + BD 18 Continue †¦ b. Obtain the simplify SOP expression from the K-map: ACD C D C D CD C D AB AB ABC 0 0 1 0 1 1 1 0 0 1 1 1 ACD 0 1 0 0 A BC AB AB Simplified SOP expression: Y = A C D + A BC + ACD + ABC 19 Continue †¦ c. Obtain the simplify SOP expression from the K-map: alternative solution: C D C D CD C D AB AB AB C D C D CD C D AB A CD 0 0 0 0 AC D 0 0 1 1 1 1 0 1 0 0 0 0 AB D 0 0 0 0 AC D 0 0 1 1 1 1 0 1 0 0 0 0 B CD A CD AB AB AB AB Y = A CD + AC D + AB D Y = A CD + AC D + B CD 20 General Terminology for Logic Minimization †¢ †¢ Here, we define four terms to provide the basis for general function minimization techniques These terms are implicant, prime implicant, essential prime implicant and cover We refer to the K-map below in explaining each term B C B C BC B C A A 1 0 1 1 3 2 1 4 1 5 1 7 6 †¢ †¢ An implicant is a product term that could be used to cover minterms of the function In the K-map above, there are 11 implicants: 5 m interms: {A B C , A BC , AB C , AB C , ABC} 5 group of two adjacent minterms: {AB , AC , A C , B C , BC} 1 group of four adjacent minterms:{C} 21 Continue †¦ †¢ †¢ †¢ A prime implicant is an implicant that is not part of any other mplicant In the K-map, there are two prime implicant: C and AB An essential prime implicant is a prime implicant that covers at least one minterm that is not covered by any other prime implicants Prime implicant AB is essential as it is the only prime implicant that covers minterm 4 Prime implicant C is also essential as it is the only prime implicant that covers minterm 1, 3 and 7 A cover of a function is a set of prime implicants for which each minterm of the function is contained in (covered by) at least one prime implicant All essential prime implicants must be used in any cover of a function 22 †¢ †¢ †¢ Continue †¦ †¢ †¢ For the K-map above, the set of implicants { AB , C} represents a cover of the fun ction A minimum cover contains the minimum number of prime implicants which contains all minterm in the function Consider the 4-variable K-map below: C D C D CD C D AB AB AB AB 1 1 Prime implicants †¢ C D C D CD C D AB AB AB 1 1 1 1 1 1 1 1 1 AB AB AB AB C D C D CD C D 1 1 1 1 Minimum cover 1 1 1 1 1 1 1 1 1 1 1 1 AB Essential prime implicants 23 Continue †¦ †¢ Consider another K-map C D C D CD C D AB AB AB AB 1 1 1 1 1 1 1 Prime implicants C D C D CD C D AB 1 1 1 1 1 1 1 1 1 1 AB AB 1 AB Essential prime implicants (minimum cover) 24 Don’t Care Conditions †¢ †¢ †¢ †¢ Some logic circuit will have certain input conditions whereby the output is unspecified This is usually because these input conditions would never occur In other words, we â€Å"don’t care† whether the output is HIGH or LOW Consider the following example: An air conditioning system has two inputs, C and H: – C will be ‘1’ if temperature is too cold (below 15 °C) Otherwise, it will be ‘0’ – H will be ‘1’ if temperature is too hot (above 25 °C) Otherwise, it will be ‘0’ – Output Y will be ‘1’ if temperature is too cold or too hot. If the temperature is acceptable, Y will be ‘0’ 25 Continue †¦ As there are two inputs, there are 4 possible logical conditions: C 0 0 1 1 H 0 1 0 1 Y 0 1 1 X meaning just nice too hot too cold ? Input condition C = 1, H = 1 has no real meaning, as it is impossible to be too hot and too cold at the same time We put a ‘X’ at the output corresponds to this input condition as this input condition cannot occur 26 K-map and Don’t Care Term †¢ Don’t care term, ‘X’ can be treated as ‘0’ or ‘1’ since they cannot occur In K-map, we can choose the don’t care term as ‘0’ or ‘1’ to our advantage A B C D Y 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 X 0 1 0 0 1 0 1 0 1 X 0 1 1 0 0 0 1 1 1 X 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 X 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 X C D C D CD C D AB AB AB 0 1 1 0 1 X 1 0 X X X X 0 0 1 0 AB Simplified Boolean expression: Y = AB + BC + A D 27 More examples †¦ C D C D CD C D AB AB AB AB C D C D CD C D AB AB AB AB 1 1 X 1 0 1 X 1 0 0 X X 0 1 X X 1 0 X 1 0 0 X 0 0 0 X X 1 X X Y = C D + BC + BD + A C D C D CD C D AB AB AB Y = B D + CD C D C D CD C D AB AB AB 0 0 1 0 1 X 1 1 0 1 X 0 0 0 0 0 1 1 X 0 1 X X 1 0 1 X X 0 0 X X 28 AB AB Y = ABC + C D + BD Y = A C + BD + AD Plotting function in Canonical Form †¢ Logic function may be expressed in many forms, ranging from simple SOP/POS expression to more complex expressions However, each of them has a unique canonical SOP/POS form If a Boolean expression is expressed in canonical form, it can be readily plotted on the K-map Consider the following Boolean expression: †¢ †¢ †¢ Y = ABC + B C Convert to canonical SOP expression: Y = ABC + B C ( A + A) = ABC + A B C + AB C 29 Continue †¦ Y = ABC + A B C + AB C Plotting the canonical SOP expression onto K-map B C B C BC B C A A 1 1 0 0 BC 0 0 0 1 AC Simplified SOP expression: Y = B C + AC †¢ Consider plotting the following Boolean expression on K-map: Y = C ( A ? B) + A + B 30 Continue †¦ First, convert to SOP expression Y = C ( A ? B) + A + B = C ( AB + A B) + A B = AB C + A BC + A B (C + C ) = AB C + A BC + A B C + A B C B C B C BC B C A A 1 0 AB 1 1 1 0 BC 0 0 AC ?Y = A B + B C + A C 31 Plotting K-map from SOP expression †¢ †¢ It is sometime too tedious to convert a Boolean expression to its canonical SOP form Consider the following Boolean expression: Y = AB (C + D )(C + D ) + A + B Convert to SOP form: Y = ( AB C + AB D )(C + D ) + A B = AB C D + AB CD + A B Convert to canonical form: Y = AB C D + AB CD + A B (C + C )( D + D) = AB C D + AB CD + ( A B C + A B C )( D + D) = AB C D + AB CD + A B C D + A B C D + A B CD + A B CD 32 Continue †¦ Y = AB C D + AB CD + A B C D + A B C D + A B CD + A B CD Plot the minterm on K-map: C D C D CD C D AB AB AB 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 AB AB B CD BC D Simplified SOP expression: Y = B C D + B CD + A B 33 Continue †¦ †¢ †¢ †¢ †¢ †¢ Boolean expression can be plotted on to the K-map from its SOP form Product terms with four variables are the minterms and correspond to a single cell on the K-map Product term with three variables corresponds to a loop of two adjacent minterms Product term with only two variables is a quad (a loop of four adjacent minterms) Product term with a single variable is an octet (a loop of eight adjacent minterms) 1 cell 2 cells Y = A + BC + B CD + ABCD 4 cells 8 cells 34 Continue †¦ †¢ Consider the previous example: Y = AB C D + AB CD + A B minterms 4 cells †¢ †¢ †¢ Both minterms are directly plotted on the K-map The loop which corresponds to A B is drawn on the K-map The cells inside the loops are filled with ‘1’ C D C D CD C D AB AB AB AB 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 AB AB C D A B CD 35 Continue †¦ †¢ Consider the following Boolean expression: Y = ( A + B )( AC + D ) Convert to SOP form: Y = AC + AD + ABC + BD Plot the SOP onto K-map C D C D CD C D AB AB AB AB AC BD C D C D CD C D AB AB ill cells in loops with ‘1’ 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 36 ABC AB AB AD Continue †¦ Obtain the simplified SOP expression from K-map: C D C D CD C D AB AB AB AB 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 Simplified SOP expression: Y = AC + AD + BD 37 Continue †¦ Example: Redesign the logic circuit below from its simplified SOP expression: A B C D Z Z = ( B + D )( B + D ) + B(CD + A D ) 38 Continue †¦ Z = ( B + D )( B + D ) + B(CD + A D ) = B + D + B + D + BCD + A BD = BD + B D + BCD + A BD C D C D CD C D AB AB AB 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 AB Z = BD + B D + A B 39 How to cite Simplification of Switching Function, Papers Simplification of Switching Function Free Essays EEN1036 Digital Logic Design Chapter 4 part I Simplification of Switching Function 1 Objective s s s s Simplifying logic circuit Minimization using Karnaugh map Using Karnaugh map to obtain simplified SOP and POS expression Five-variable Karnaugh map 2 Simplifying Logic Circuits †¢ †¢ †¢ A A Boolean expression for a logic circuit may be reduced to a simpler form The simplified expression can then be used to implement a circuit equivalent to the original circuit Consider the following example: B C A B C + A BC Y AB C + AB C Y = A B C + A BC + AB C + AB C 3 Continue †¦ Checking for common factor: Y = A B C + A BC + AB C + AB C = A C ( B + B ) + AB (C + C ) Reduce the complement pairs to ‘1’ Y = A C ( B + B ) + AB (C + C ) = A C + AB Draw the circuit based on the simplified expression A B C Y 4 Continue †¦ †¢ A Consider another logic circuit: B C Y Y = C( A + B + C ) + A + C Convert to SOP expression: Y = C( A + B + C ) + A + C = AC + B C + AC Checking for common factor: Y = A(C + C ) + B C = A + BC 5 Continue †¦ †¢ †¢ Simplification of logic circuit algebraically is not always an easy task The following two steps might be useful: i. The original expression is convert into the SOP form by repeated application of DeMorgan’s theorems and multiplication of terms ii. The product terms are then checked for common factors, and factoring is performed wherever possible 6 Continue †¦ †¢ Consider the truth table below: A 0 0 0 0 1 B 0 0 1 1 0 C 0 1 0 1 0 Y 0 0 1 0 0 Minterm Boolean expression: Simplify to yield: Y = A BC + ABC + AB C Y = BC ( A + A) + AB C = BC + AB C 1 0 1 1 1 1 0 1 1 1 1 0 †¢ If minterms are only differed by one bit, they can be simplified, e. We will write a custom essay sample on Simplification of Switching Function or any similar topic only for you Order Now g. A BC ABC 7 Continue †¦ †¢ More example: A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 Y 0 1 1 0 0 1 1 0 Minterm Boolean expression: Y = A B C + A BC + AB C + ABC Minterms 1 and 5, 2 and 6 are only differ by one bit: Y = B C ( A + A) + BC ( A + A) = BC + B C A B C Y 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 Minterm Boolean expression: Y = A B C + A BC + AB C + ABC Checking and factoring minterms differed by only by one bit: Y = A C ( B + B ) + AC ( B + B ) = A C + AC = C ( A + A) =C 8 Continue †¦ †¢ †¢ †¢ Though truth table can help us to detect minterms which are only differed by one bit, it is not arranged in a proper way A Karnaugh map (K-map) is a tool, which help us to detect and simplify minterms graphically It is a rearrangement of the truth table where each adjacent cell is only differed by one bit By looping adjacent minterms, it is similar to grouping the minterms with a single bit difference on the truth table 9 K arnaugh Map †¢ †¢ A K-map is just a rearrangement of truth table, so that minterms with a single-bit difference can be detected easily Figure below shows 4 possible arrangement of 3-variable K-map A BC 0 0 01 1 11 3 10 2 C AB 00 0 01 2 11 6 10 4 0 1 4 5 7 6 0 1 1 3 7 5 AB C 0 0 1 1 BC A 0 0 1 4 00 01 2 3 00 01 1 5 11 6 7 11 3 7 10 4 5 10 2 6 10 Continue †¦ †¢ Figure below show two possible arrangement of 4variable K-map CD AB 00 0 01 1 11 3 10 2 AB 00 CD 01 4 11 12 10 8 00 01 4 5 7 6 00 0 01 1 5 13 9 11 12 13 15 14 11 3 7 15 11 10 8 9 11 10 10 2 6 14 10 †¢ Notice that the K-map is labeled so that horizontally and vertically adjacent cells differ only by one bit. 11 Continue †¦ †¢ The K-map for both SOP and POS form are shown below: C D C D CD C D AB AB AB 0 1 3 2 C+D C+ D C + D C +D A +B 0 1 3 2 4 5 7 6 A+B A+B A +B 4 5 7 6 12 13 15 14 12 13 15 14 AB 8 9 11 10 8 9 11 10 SOP form (minterm) POS form (maxterm) †¢ †¢ The simplified SOP expression can be obtained by properly combining those adjacent cells which contains ‘1’ This process of combining adjacent minterms is known as 12 looping Continue †¦ †¢ †¢ Each loop of minterms will form a group which can be represented by a product term When a variable appears in both complemented and uncomplemented form within a group, that variable is eliminated from the product term C D C D CD C D AB AB AB AB 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 group 2 group 1: C D( AB + AB ) = AC D group 2: AB(C D + CD ) = ABD Simplified SOP expression: Y = AC D + ABD 13 group 1 Continue †¦ †¢ Consider another K-map: C D C D CD C D AB AB AB AB 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 group 1 C D C D CD C D AB AB AB AB 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 14 group 1: ( A B + AB )(C D + CD ) = BD Simplified SOP expression: Y = BD group 1: C D ( A B + A B + AB + AB ) = C D Simplified SOP expression: Y = CD group 1 From truth table to K-map †¢ The content of each cell can be directly plot on the Kmap according to the truth table Consider the following example: 0 1 2 3 4 5 6 7 A 0 0 0 0 1 1 1 1 B C Y 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 B C B C BC B C A A 1 0 1 1 0 3 1 2 0 4 0 5 0 7 1 6 AB BC Simplified SOP expression: Y = A B + BC 15 Continue †¦ †¢ Consider the following 4-variable K-map A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C D Y 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 C D C D CD C D AB AB AB 0 0 0 1 1 1 0 1 0 0 1 0 3 0 0 0 ACD 2 4 5 7 6 12 13 15 14 AB 0 8 9 11 0 10 ABD Simplified SOP expression: Y = A C D + ABD 16 Continue †¦ †¢ Some guidelines: i. Construct K-map and fill it according to the truth table ii. Only loop cells in the power of 2, i. e. 2 cells, 4 cells, 8 cells and so on iii. Always start by looping the isolated minterms iv. Look for minterms which are adjacent to only one minterm and loop them together v. Proceed on to loop the largest possible groups, from eight minterms (octet), 4 minterms (quad) to 2 minterms (pair) vi. Obtain the product term for each group vii. The sum of these product terms will be the simplified SOP expression 17 Continue †¦ Example: a. Obtain the simplify SOP expression for the truth table: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Y 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 C D C D CD C D AB AB AB AB A B CD 0 0 0 0 0 0 1 1 0 1 0 1 1 3 1 0 0 0 2 4 5 7 6 12 13 15 14 8 9 1 11 10 BD ACD Simplified SOP expression: Y = A B CD + ACD + BD 18 Continue †¦ b. Obtain the simplify SOP expression from the K-map: ACD C D C D CD C D AB AB ABC 0 0 1 0 1 1 1 0 0 1 1 1 ACD 0 1 0 0 A BC AB AB Simplified SOP expression: Y = A C D + A BC + ACD + ABC 19 Continue †¦ c. Obtain the simplify SOP expression from the K-map: alternative solution: C D C D CD C D AB AB AB C D C D CD C D AB A CD 0 0 0 0 AC D 0 0 1 1 1 1 0 1 0 0 0 0 AB D 0 0 0 0 AC D 0 0 1 1 1 1 0 1 0 0 0 0 B CD A CD AB AB AB AB Y = A CD + AC D + AB D Y = A CD + AC D + B CD 20 General Terminology for Logic Minimization †¢ †¢ Here, we define four terms to provide the basis for general function minimization techniques These terms are implicant, prime implicant, essential prime implicant and cover We refer to the K-map below in explaining each term B C B C BC B C A A 1 0 1 1 3 2 1 4 1 5 1 7 6 †¢ †¢ An implicant is a product term that could be used to cover minterms of the function In the K-map above, there are 11 implicants: 5 m interms: {A B C , A BC , AB C , AB C , ABC} 5 group of two adjacent minterms: {AB , AC , A C , B C , BC} 1 group of four adjacent minterms:{C} 21 Continue †¦ †¢ †¢ †¢ A prime implicant is an implicant that is not part of any other mplicant In the K-map, there are two prime implicant: C and AB An essential prime implicant is a prime implicant that covers at least one minterm that is not covered by any other prime implicants Prime implicant AB is essential as it is the only prime implicant that covers minterm 4 Prime implicant C is also essential as it is the only prime implicant that covers minterm 1, 3 and 7 A cover of a function is a set of prime implicants for which each minterm of the function is contained in (covered by) at least one prime implicant All essential prime implicants must be used in any cover of a function 22 †¢ †¢ †¢ Continue †¦ †¢ †¢ For the K-map above, the set of implicants { AB , C} represents a cover of the fun ction A minimum cover contains the minimum number of prime implicants which contains all minterm in the function Consider the 4-variable K-map below: C D C D CD C D AB AB AB AB 1 1 Prime implicants †¢ C D C D CD C D AB AB AB 1 1 1 1 1 1 1 1 1 AB AB AB AB C D C D CD C D 1 1 1 1 Minimum cover 1 1 1 1 1 1 1 1 1 1 1 1 AB Essential prime implicants 23 Continue †¦ †¢ Consider another K-map C D C D CD C D AB AB AB AB 1 1 1 1 1 1 1 Prime implicants C D C D CD C D AB 1 1 1 1 1 1 1 1 1 1 AB AB 1 AB Essential prime implicants (minimum cover) 24 Don’t Care Conditions †¢ †¢ †¢ †¢ Some logic circuit will have certain input conditions whereby the output is unspecified This is usually because these input conditions would never occur In other words, we â€Å"don’t care† whether the output is HIGH or LOW Consider the following example: An air conditioning system has two inputs, C and H: – C will be ‘1’ if temperature is too cold (below 15 °C) Otherwise, it will be ‘0’ – H will be ‘1’ if temperature is too hot (above 25 °C) Otherwise, it will be ‘0’ – Output Y will be ‘1’ if temperature is too cold or too hot. If the temperature is acceptable, Y will be ‘0’ 25 Continue †¦ As there are two inputs, there are 4 possible logical conditions: C 0 0 1 1 H 0 1 0 1 Y 0 1 1 X meaning just nice too hot too cold ? Input condition C = 1, H = 1 has no real meaning, as it is impossible to be too hot and too cold at the same time We put a ‘X’ at the output corresponds to this input condition as this input condition cannot occur 26 K-map and Don’t Care Term †¢ Don’t care term, ‘X’ can be treated as ‘0’ or ‘1’ since they cannot occur In K-map, we can choose the don’t care term as ‘0’ or ‘1’ to our advantage A B C D Y 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 X 0 1 0 0 1 0 1 0 1 X 0 1 1 0 0 0 1 1 1 X 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 X 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 X C D C D CD C D AB AB AB 0 1 1 0 1 X 1 0 X X X X 0 0 1 0 AB Simplified Boolean expression: Y = AB + BC + A D 27 More examples †¦ C D C D CD C D AB AB AB AB C D C D CD C D AB AB AB AB 1 1 X 1 0 1 X 1 0 0 X X 0 1 X X 1 0 X 1 0 0 X 0 0 0 X X 1 X X Y = C D + BC + BD + A C D C D CD C D AB AB AB Y = B D + CD C D C D CD C D AB AB AB 0 0 1 0 1 X 1 1 0 1 X 0 0 0 0 0 1 1 X 0 1 X X 1 0 1 X X 0 0 X X 28 AB AB Y = ABC + C D + BD Y = A C + BD + AD Plotting function in Canonical Form †¢ Logic function may be expressed in many forms, ranging from simple SOP/POS expression to more complex expressions However, each of them has a unique canonical SOP/POS form If a Boolean expression is expressed in canonical form, it can be readily plotted on the K-map Consider the following Boolean expression: †¢ †¢ †¢ Y = ABC + B C Convert to canonical SOP expression: Y = ABC + B C ( A + A) = ABC + A B C + AB C 29 Continue †¦ Y = ABC + A B C + AB C Plotting the canonical SOP expression onto K-map B C B C BC B C A A 1 1 0 0 BC 0 0 0 1 AC Simplified SOP expression: Y = B C + AC †¢ Consider plotting the following Boolean expression on K-map: Y = C ( A ? B) + A + B 30 Continue †¦ First, convert to SOP expression Y = C ( A ? B) + A + B = C ( AB + A B) + A B = AB C + A BC + A B (C + C ) = AB C + A BC + A B C + A B C B C B C BC B C A A 1 0 AB 1 1 1 0 BC 0 0 AC ?Y = A B + B C + A C 31 Plotting K-map from SOP expression †¢ †¢ It is sometime too tedious to convert a Boolean expression to its canonical SOP form Consider the following Boolean expression: Y = AB (C + D )(C + D ) + A + B Convert to SOP form: Y = ( AB C + AB D )(C + D ) + A B = AB C D + AB CD + A B Convert to canonical form: Y = AB C D + AB CD + A B (C + C )( D + D) = AB C D + AB CD + ( A B C + A B C )( D + D) = AB C D + AB CD + A B C D + A B C D + A B CD + A B CD 32 Continue †¦ Y = AB C D + AB CD + A B C D + A B C D + A B CD + A B CD Plot the minterm on K-map: C D C D CD C D AB AB AB 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 AB AB B CD BC D Simplified SOP expression: Y = B C D + B CD + A B 33 Continue †¦ †¢ †¢ †¢ †¢ †¢ Boolean expression can be plotted on to the K-map from its SOP form Product terms with four variables are the minterms and correspond to a single cell on the K-map Product term with three variables corresponds to a loop of two adjacent minterms Product term with only two variables is a quad (a loop of four adjacent minterms) Product term with a single variable is an octet (a loop of eight adjacent minterms) 1 cell 2 cells Y = A + BC + B CD + ABCD 4 cells 8 cells 34 Continue †¦ †¢ Consider the previous example: Y = AB C D + AB CD + A B minterms 4 cells †¢ †¢ †¢ Both minterms are directly plotted on the K-map The loop which corresponds to A B is drawn on the K-map The cells inside the loops are filled with ‘1’ C D C D CD C D AB AB AB AB 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 AB AB C D A B CD 35 Continue †¦ †¢ Consider the following Boolean expression: Y = ( A + B )( AC + D ) Convert to SOP form: Y = AC + AD + ABC + BD Plot the SOP onto K-map C D C D CD C D AB AB AB AB AC BD C D C D CD C D AB AB ill cells in loops with ‘1’ 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 36 ABC AB AB AD Continue †¦ Obtain the simplified SOP expression from K-map: C D C D CD C D AB AB AB AB 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 Simplified SOP expression: Y = AC + AD + BD 37 Continue †¦ Example: Redesign the logic circuit below from its simplified SOP expression: A B C D Z Z = ( B + D )( B + D ) + B(CD + A D ) 38 Continue †¦ Z = ( B + D )( B + D ) + B(CD + A D ) = B + D + B + D + BCD + A BD = BD + B D + BCD + A BD C D C D CD C D AB AB AB 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 AB Z = BD + B D + A B 39 How to cite Simplification of Switching Function, Essay examples

Outcome

Outcome-Based Education Essay Outcome-based Education Denied Joan M. Montana, R. N. Outcome-based education Is the trend In todays curriculum. It Is currently favored Internationally In countries such as Canada, South Africa, New Zealand, and united States (Milan, 2004, cited by Butler, 2004). Outcome-based education encompasses learning at the students pace to achieve a desired outcome. It is defined by Chary (2003) as a method of curriculum design and teaching that focuses on what students can actually do after they are taught. Basically, it puts emphasis on measuring what the students have learned and understand after a rouser by not merely giving examinations but rather, activities that assess critical thinking of the students. In this light, outcome-based education is beneficial to our educational system In providing professional and competent workers. Biggs and Tang (2007) stated that It Is beneficial to the students since the learning outcome tell them precisely not only what they are supposing to be learning, but how and to what standard. In the development of outcome-based education, educators studied the work of Carroll and Bloom. Carroll said that it was inappropriate to fix the time for study and expect variable learning results from students (Davis, 2003). Bloom developed Carols thinking into the notion of mastery learning, in which a fixed level of performance was to be achieved by students by changing the relationship between time and learning (Davis, 2003). From this, the underlying principle of outcome-based education was achieved in a sense that the learning became fixed and the time to achieve the learning became the variable. The primary aim of outcome-based education Is to facilitate desired changes within the learners, by Increasing knowledge, developing skills and/or positively Influencing attitudes, values and Judgment (Butler, 2004). As a whole, It targets the cognitive, affective and psychosomatic domains of learning, thus, facilitating better understanding and retention of the topics learned. As stated by Killeen (2000), outcome-based learning is underpinned by three basic premises: All students can learn and succeed, but not all in the same time or in the same way. Successful learning promotes even more successful learning. * Schools (and teachers) control the conditions that determine whether or not students are successful at school learning. Spade and his colleagues (cited by Lawson ; Easels-Williams, 2007) identifies four organizing principles of OBOE, namely: (1) clarity of focus; (2) designing back; (3) high expectation for all students; and (4) capability of the teachers to provide expanded opportunities to allow for achievement of outcomes In a variety of ways. In clarity of focus, the learning outcomes broad and specific must be clearly Identified for the students; and all teaching and learning actively must be aligned with these outcomes. In designing back, the curriculum content should flow clearly from the most general valued outcomes, to the related, ore special outcomes, to class lesson actively. In Nell expectations Tort all students, it requires that successful and challenging learning experiences and achievement of high standards be part of learning for all students. In the fourth principle, it is suggested that different learners may take different routes, and different amounts of time or different numbers of attempts, to achieve the same outcome. Moreover, visionary elements, proposed by Spade (cited by Lawson ; Easels-Williams, 2007) emphasized the need for educational leaders to engage in empowerment thinking, visionary thinking and future-focused thinking that looks to the world as it should be in the future. Killeen (2000) acknowledged the significance of using outcomes to guide instructional planning. He claimed that there are three major steps in an OBOE system. These steps includes: deciding on the outcomes that students are to achieve; deciding how to assist students to achieve those outcome and deciding how to determine when students have achieved the outcomes. In addition, teaching strategies for OBOE is said to vary in numerous ways. Whatever approach to teaching will be used, it is important for educators to keep the following points in mind: * The main focus should be on learning rather than teaching Students cannot not learn when if they do not think * Thinking is facilitated and encouraged by the processes that were being used with the contents as well as by the content itself. The subject does not exist in isolation -educators should have to help students make links to other subject. * Educators have the main responsibility to help students learn how to learn. On the other hand, students also have responsibilities for learning in an OBOE system. Cookbook (1997, as cited by Killeen, 2000) suggest that learners are responsible for th eir own learning and progress. The principle acknowledges the fact that learning is ultimately a personal and an internal event. Students must be motivated if they are to learn. .u5125200dd93ef216613ea39f29f6407e , .u5125200dd93ef216613ea39f29f6407e .postImageUrl , .u5125200dd93ef216613ea39f29f6407e .centered-text-area { min-height: 80px; position: relative; } .u5125200dd93ef216613ea39f29f6407e , .u5125200dd93ef216613ea39f29f6407e:hover , .u5125200dd93ef216613ea39f29f6407e:visited , .u5125200dd93ef216613ea39f29f6407e:active { border:0!important; } .u5125200dd93ef216613ea39f29f6407e .clearfix:after { content: ""; display: table; clear: both; } .u5125200dd93ef216613ea39f29f6407e { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u5125200dd93ef216613ea39f29f6407e:active , .u5125200dd93ef216613ea39f29f6407e:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u5125200dd93ef216613ea39f29f6407e .centered-text-area { width: 100%; position: relative ; } .u5125200dd93ef216613ea39f29f6407e .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u5125200dd93ef216613ea39f29f6407e .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u5125200dd93ef216613ea39f29f6407e .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u5125200dd93ef216613ea39f29f6407e:hover .ctaButton { background-color: #34495E!important; } .u5125200dd93ef216613ea39f29f6407e .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u5125200dd93ef216613ea39f29f6407e .u5125200dd93ef216613ea39f29f6407e-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u5125200dd93ef216613ea39f29f6407e:after { content: ""; display: block; clear: both; } READ: What is culture? Argumentative EssayKilleen (2000) summarized three main points in the importance of motivating: students need to know why they are learning whatever they are learning, they need to see some value in this learning, and they need to believe that they can be successful. Outcome-based education allows the students to learn independently at heir own pace, having an outcome to achieve at the end of the learning process. The teachers are merely facilitators of learning guiding and assisting students to understand information and to transform it into their own personal knowledge. Outcome-based education, as a trend in the present curriculum, has its advantages and disadvantages. Mostly, students would benefit from this system. As stated by Razorblades and Uncharismatic (2013), OBOE encourages self-directed learning and allow the students to have a meta-cognitive understanding of the educational program and their role in that process. It also helps students to become aware of what they should be learning, aware of what they are actually learning, and aware of the control that they have over their own learning (Killeen, 2000). In contrast to its benefits, critics of OBOE pointed out several disadvantages. One is stated by Razorblades and Uncharismatic (2013) that OBOE conflicts with the wonderful, unpredictable voyages of exploration that characterize learning through discovery and inquiry. Another is that it is too technical or mechanical or inflexible such that innovation and creativity of the teachers would be killed. Furthermore, it emphasizes minimum levels of achievement and thus encourages mediocrity. However, these can De met Day OBOE In ten sense Tanat teachers would a De addle to practice Innovation Ana creativity in developing teaching strategies that would help the students achieve the outcomes. In terms of mediocrity, OBOE emphasizes the principle of high expectations for all the students wherein the teacher must set the criteria for the outcomes. It can be said that one of the major disadvantage of OBOE is the burden to the teachers in terms of findings ways to help the students arrive at the desired outcomes. In inclusion, outcome based education upgrades the educational system in terms of student involvement in the learning process, and promotes higher level of functioning after the learning process.

Gavin Degraw - Chariot free essay sample

Gavin Degraw Chariot Those screaming tweens could never get in the way of me singing along with that bluesy folk-style music Gavin Degraw creates. Gavin Degraw live had to be one of the most amazing experiences of my life. The man grabs your heart and tugs at those strings. The ones you thought you could never even feel being bothered with. As I looked around in the audience that night of the concert, I couldnt look one way without seeing a fan belting out their lungs. The fans of Gavin Degraw are true and real, and loyal to thier hero. The look he has as he performs; it shows a sign of weakness but security. He has that sly confidence about him that just makes you love him. And his voice? Dont even get me started. Just think Marvin Gaye, Barry Manilow, Micahel Buble. But all of them, together, only twenty times better. We will write a custom essay sample on Gavin Degraw Chariot or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Degraws music has gotten me through so much in life. I was depressed, his caring words brightened up my day. That small tap of the foot his music brings on could make all the difference in the world. I could go on forever about him. My dream is to meet him, and that I will never let go. Degraw makes me dream of how the world can be better. His lyrics, which by the way, he writes his self, help you indulge the real world and how we all really want better lives, and we can have them in this colorful world. I dont wanna be anything other than what Ive been trying to be lately, neither do I, neither do I.

the Red Violin essays

the Red Violin essays The Red Violin offers some interesting messages about the universality of the language of music. The acting and sets are spectacular, and the actors through the eras do very credible jobs of playing the magical violin. Lastly, the secret of the red violin's color turns out to be an apt symbol for the level of commitment that true musical devotion demands. "The Red Violin" takes its audience on a journey spanning five countries and three centuries. As the violin passes into five principal lives, each tells a story of both hope and greed. Violin maker Nicolo, set aside his best violin as a gift to his unborn child. His wife Anna inquires from her housekeeper and Tarot reader about the child's life. Anna is instructed to choose five cards. As each card in interpreted, we follow the "life" of the violin as it interacts with each person who eventually possesses it. Through the tragedy of Anna and her child's death, we learn the card reading is also for the Red Violincall it Bussotti's other child. Hope turns to grief as the perfect violin is all that remains of everything dear to Nicolo. Painting the violin red, he pours his anger into it. He wanted to leave as his legacy a child of great musical capacity, and through the embodiment of his violin, he did. The Red Violin resurfaces in an Austrian monastery where it chances into the hands of a prodigy of exceptional abilitysix-year-old Kaspar . In 1792, the monks summon Georges, a master of the period, to groom the child. Just as Kaspar is to perform for the patron Georges has arranged young Kaspar's weak and frail heart fails him at his pivotal moment and promise turns to setback in a heart beat. In 1893, in Oxford England, gypsies playing the Red Violin beckon the ear of the flamboyant romantic musician Frederick Pope. Feeling aroused to play, he summons his lover, the novelist Victoria Byrd. Seduced by the travels her novel propels her on, Russia becomes Victoria's next con...

Accounting Theory - Comparison between Positive and Normative Approach Essay

Accounting Theory - Comparison between Positive and Normative Approach - Essay Example The study of accounting theory enables to understand our past and provide us with a positive reception of how our recent practices and problems came into being. A historical investigation also tells that certain problems are continuing and may not be capable of an everlasting solution, for example, accounting for intangible and changing price levels. The accounting theory’s development came up because of needs and changes in accounting concepts and techniques. The main purpose of accounting is to plan periodic matching of revenues and cost. The accounting theory is classified into positive and normative accounting theory. This paper will take into consideration the positive and negative approach of accounting theories; their advantages and disadvantages, comparison and relationships between the two and evidence supporting that where each of the approaches might be appropriate in the current economic and business environment. Positive Approach The positive approach in accountin g starts with observations of financial information of business firms and on the basis of recurring relationships proceeds to draw overview and principles of accounting. Financial and accounting information, hence, represents recurring relationships leads to the formulation of principles. Different steps involved in positive accounting theory are: doing the observations and then recording of all the observations, analysis and then doing classification of these observations in order to detect recurring relationships, inductive derivation of principles of accounting and generalizations from those observations which signify recurring relationships and last step is the testing of generalizations (Rao, 2006, p.57). This approach is appropriate in the business environment in order to explain and forecast management’s choice of standards through analysing the benefits and costs of particular financial exposures in relation to allocation of resources and to various individuals within the economy. This theory is based on the propositions that shareholders, managers, and politicians or regulators are rational and that they try to make the best use of their utility, which is related to their reward and therefore to their wealth. The preference of an accounting policy by any of these groups depends on a comparison of the relative benefits and costs of different accounting procedures in such a way so as to maximize their utility. For example, it will be appropriate in such a business environment where it is assumed that management takes into consideration the effects of the reported accounting of numbers on political cost, information production cost, tax regulation, management compensation, and constraints found in bond-indenture provisions. The fundamental idea of the positive theory is to develop hypotheses about factors that persuade the accounting practices and to test the legality of these hypotheses empirically.     

Does diversity of opinion in the press matter any more, now we have Essay

Does diversity of opinion in the press matter any more, now we have access to participatory and social media - Essay Example As more users are turning towards opting new technologies and social media websites, and are showing reluctant behaviour towards reading newspapers. One possible reason for less circulation of newspaper today can be because of the ease that technology has provided. As with the innovations in the technology and the ease it provided for the masses in terms of using electronic gadgets, mobile phones and connecting online, the productivity of newspapers and print media have undergone decreases. More people are relying on internet and social media websites for the purpose of news, with it they are always connected to the internet and can read timely news, as this new medium (internet) is believe to be the fastest source of providing information or serving the purpose of communication. Furthermore, this medium also enhances the concept of diversification of opinion, as users around the world feel connected with each other and can share their views with the masses in no time. Moreover they can read or listen to the views posted by others, which at times gives them new perception to think about the same issue (Van Djick, 2009). Current Situation: Likewise in a recent past majority of newspapers from the United Kingdom and America were forced to follow the downsizing policy (2008). As a result significant numbers of employees who were working for the different newspapers were terminated, many prophesized the reasons behind these terminations were financial crisis, whereas others convicted internet and social media websites for these firings in the print media industry (Compton and Benedetti, 2010). However, there are many who have different perception in this regard, these individuals optimistically analyze these situations and believe that albeit social media websites and blogs have resulted in confining the role of newspapers and magazines but it has also resulted in providing more information and a variety of difference of opinions for the viewers (Compton and Benede tti, 2010). Meanwhile, it took a while in order to confine the long run and monopoly of newspapers and print media, as the relatively new medium (internet) is garnering more importance on the daily basis and conditions are ameliorating (Compton and Benedetti, 2010). At present print media is facing deteriorating conditions, majority of newspapers around the world are devising strategies in order to cope up with the financial turmoil and are also keen on enhancing or increasing their newspaper circulations. For instance, newspaper industry in the United Kingdom and North America reflect the situation of turmoil as many newspapers are facing bankruptcy, or are in a position where it is hard to manage their current expenses because of high cost involved in the system, there are some who ended their journey in this regard and some are knocking the doors or are in the verge of facing a serious collapse. Some prominent names of the newspaper industry of America, which were enlightening an d were sharing difference of opinions over the passage of time, are the best examples of this catastrophe. American newspaper Denver's Rocky Mountain News are history, on the other hand, The Philadelphia Inquirer, Chicago Tribune and The Los Angeles Times are amongst those newspapers which are facing serious financial catastrophe or in other words are

The Nature Of Biomedical Waste Environmental Sciences Essay

The Nature Of Biomedical Waste Environmental Sciences Essay Biomedical waste is that waste which is generated by the diagnosis and treatment of human beings or animals or by the medical research activities conducted or during the production of medical equipment. Biomedical waste can be hazardous and infectious by nature. So it needs to be handled properly to ensure it doesnt deteriorate peoples health when its discarded. Any inadequacy in the management of biomedical waste can result in the following issues: The waste can become a breeding ground for flies Can result in high risk of infections to medical staff Increased hazardous risk for the person handling the chemicals and other waste including the sharps Poor infection control can also lead to spread of infections to patients from the medical centres If such waste is reused, it can result in diseases like cholera, plague, tuberculosis, AIDS etc. Also, studies have shown that one-third of the total waste generated in the medical establishment is hazardous and toxic in nature. Since the mismanagement of biomedical waste can be dangerous to the public, the government (Ministry of Environment and Forests) has provided uniform guidelines and code of practice for the whole nation regarding the management handling of biomedical waste in the Bio-medical Waste (Management and Handling) Rules,1998. Methodology: For this project, I visited the medical centre in Symbiosis Viman Nagar Campus (SVC) for information and interviewed the doctor in charge of the centre Dr. Kiran Mahajan. Though he stated that the medical centre of SVC was not performing advanced medical treatments and thus the composition of their centres biomedical waste would differ a lot from that of a hospital, still he had the knowledge of the waste generated in hospitals and how is it managed. So we could rely on his information. So the most important source of information for this project was the interview with Dr. Kiran Mahajan and secondly, I also looked up the internet for some additional information and facts to enrich my knowledge about biomedical waste. Some of the important questions I asked Dr. Kiran Mahajan were: Q- What are the items included in (or composition of) biomedical waste? Q- How can it become dangerous if not managed well? Q- What is the process of managing biomedical waste? Q- Is this process different from the management of other waste? Q- What is the present condition of biomedical waste management in the medical institutions? Q- Can you find out any inefficiencies in the waste management process? Q- Can you quantify the amount of biomedical waste generated? Q- How is the generated waste treated/disposed off? Findings: I was enlightened with the following information by Dr. Kiran Mahajan and the internet. First of all, biomedical waste includes: Human anatomical waste (tissues, organs, body parts etc.) Animal waste (as above, generated during research/experimentation, from veterinary hospitals etc.) Microbiology and biotechnology waste, such as, laboratory cultures, micro-organisms Human and animal cell cultures, toxins etc. Waste sharps, such as, hypodermic needles, syringes, scalpels, broken glass etc. Discarded medicines Soiled waste, such as dressing, bandages, material contaminated with blood etc. Solid waste (disposable items like tubes, catheters etc. excluding sharps), Liquid waste generated from any of the infected areas, Incineration ash, Chemical waste. The management issues in bio-medical waste handling are: Reduction of waste generation Segregation of waste at the place of its generation Transportation of the waste Handling of the waste Proper disposal Stages of biomedical waste management: Stage 1: Waste generation and storage: Here the waste generated is segregated at the place of its generation and the toxic and hazardous waste is kept in a separate container which is labelled for its easy identification. Each type of waste generated is kept separately and labelled which further helps in its transportation and handling. According to the rules of the government, untreated waste shouldnt be stored beyond a point of 48 hours. Suggestions for segregation and storages of waste in separate containers: à ¢Ã¢â€š ¬Ã‚ ¢ The container must be strong enough to be able to handle the pre-determined maximum capacity of waste without any damage. à ¢Ã¢â€š ¬Ã‚ ¢ It shouldnt have any leakages. à ¢Ã¢â€š ¬Ã‚ ¢ The containers should be covered when idle. à ¢Ã¢â€š ¬Ã‚ ¢ The sharps must be stored in puncture proof containers after being mutilated. After a bag or container is sealed, a label of the name of the component should be attached to it. Stage 2: Transportation: à ¢Ã¢â€š ¬Ã‚ ¢ While collecting waste from the medical establishments, it should be ensured that the waste is properly collected without any leakages and ambiguity in its nature. à ¢Ã¢â€š ¬Ã‚ ¢ Attempts can be made to provide a separate corridor for transfer of waste from the storage area to its transport area (It can be ensured that this path is not used for mobility of the patients and visitors). Stage 3: Waste treatment and disposal: The various ways for treatment and disposal of waste are: Incineration: Its the practice of using thermal energy to convert the waste into inert materials and gases. This process has been recommended for human anatomical waste, animal waste, discarded medicines. Autoclave treatment: It is a process in which the waste material is brought in contact with steam for a time period which is sufficient to disinfect the waste material. It is recommended for biotechnology waste, waste sharps. Microwave treatment: It is again a wet thermal disinfection technology but unlike others (which heat the waste externally), microwave heats the target material inside out providing a high level of disinfection. Chemical disinfecting: It involves the use of chemicals like hypochlorite solution to disinfect the waste. It is recommended for waste sharps, solid, liquid as well as chemical wastes. Sanitary and secured landfilling: It is required in the following circumstances: Deep burial of human anatomical waste when a proper facility of incineration is not available. (Sanitary landfill) Animal waste. (Sanitary landfill) Disposal of autoclaved, microwaved waste. (Sanitary landfill) Disposal of incineration ash. (Sanitary landfill) Disposal of bio-medical waste till such time when proper treatment and disposal facility is in place. (Secured landfill) Disposal of sharps. (Secured landfill) General waste: The other non-toxic and non-hazardous waste can be taken care of by the following ways: Composting of green waste Recycling of packaging material Problems/inefficiencies being faced in the field: Some of the problems/inefficiencies being encountered in the management of biomedical waste are: Till now, it has been observed that the statistics presented in the government by the Ministry of environment and forests about the quantity of biomedical waste are often not true/accurate.* (See references for source) The Ministry of environment and forests claims that India treats more than 70% of the biomedical waste it generates (which can be misleading if the statistics are wrong as mentioned above). Another problem being faced is the improper disposal of this waste i.e. even though the correct method is being followed; the method is not being implemented properly. For. E.g. the incineration of waste is observed to be done at 400 C which is to be done at 1000 C resulting in release of poisonous gases.