# 2-17-11 - Boolean Algebra A 0=A A.1=A A A = 1 A A = 0 1 A=1...

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Boolean Algebra A + 0 = A A + A’ = 1 A . 1 = A A. A’ = 0 1 + A = 1 A + B = B + A 0. A = 0 A . B = B . A A + (B + C) = (A + B) + C A. (B. C) = (A. B). C A + A = A A . A = A A. (B + C) = A.B + A.C Distributive Law A + B.C = (A+B). (A+C) A . B = A + B De Morgan’s theorem A + B = A . B

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De Morgan’s theorem A . B = A + B A + B = A . B Thus, is equivalent to Verify it using truth tables. Similarly, is equivalent to These can be generalized to more than two variables: to A. B. C = A + B + C A + B + C = A . B . C
Synthesis of logic circuits Many problems of logic design can be specified using a truth table. Give such a table, can you design the logic circuit? Design a logic circuit with three inputs A, B, C and one output F such that F=1 only when a majority of the inputs is equal to 1. A B C F Sum of product form 0 0 0 0 F = A.B.C + A.B.C + A.B.C + A.B.C 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Draw a logic circuit to generate F

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2-17-11 - Boolean Algebra A 0=A A.1=A A A = 1 A A = 0 1 A=1...

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