HW1_Solution - Homework 1 Solution 1 Simplify the following...

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Homework 1 Solution 1. Simplify the following expressions using Boolean algebra theorems. a) b) Solution: a ) AB’C’+A’B’+C =AB’C’+A’B’+( AB’C+C ) [covering] =( AB’C’+AB’C )+A’B’ +C [associativity] = AB’ +A’B’ +C [combining] = B’ +C [combining] b) A’+B’+C’+D’+ABCD = (ABCD)’ +ABCD [De Morgan] =1 [combining] 2. Prove NAND operation is not associative using perfect induction, namely: ) ) )) Solution: A B C 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 ) ) 1 0 1 0 1 0 1 1 )) 1 1 1 1 0 0 0 1 3. Write both canonical sum-of-products and canonical product-of-sums for each of the following functions: a) ) b) ) Solution: a) ) ) ) ) ) ) ) ) ) ) ) b) ) ) ) ) ) ) 4. Use Karnaugh maps to determine an expression for the minimal sum-of-products and the minimal product-of-sums for each of the following functions (dc = Don’t Care). a) ) ) b) ) )
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a) ) ) ) b) ) ) ) )
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5. Design a locking system with 3 inputs (A, B, C) and 2 outputs (F, G). F is the unlock signal, which will be 1 if and only if all the inputs are 1. G is the alarm signal, which will be 1 if two or more inputs are 1.
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