HW1_Solution

# C using a karnaugh map determine the outputs as a

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Unformatted text preview: s of the circuit as a canonical sum-of-products. c) Using a Karnaugh map, determine the outputs as a minimal sum-of-products. Solution: a) 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 F 0 0 0 0 0 0 0 1 G 0 0 0 1 0 1 1 1 b) , c) For F, since there is only 1 input combination of ABC that outputs 1, For G: 6. Determine and simplify the logic expression for the following circuits. a) Solution: a) F=(((AB)’)’+B’)’ =(AB+B’)’ [involution] b) . =(AB)’B =(A’+B’)B =A’B+B’B =A’B [De Morgan] [De Morgan] [distributivity] [complements] b) F=((A’B)’(B(ABC)’)’((ABC)’C)’)’ =A’B+B(ABC)’+(ABC)’C [De Morgan] =A’B+B(A’+B’+C’)+(A’+B’+C’)C [De Morgan] =A’B+BA’+BB’+BC’+A’C+B’C+C’C [distributivity] =A’B+A’B+BB’+BC’+A’C+B’C+C’C [commutativity] =A’B+BB’+BC’+A’C+B’C+C’C [idempotency] =A’B+BC’+A’C+B’C [complements] =(A’B+B’C+A’C)+BC’ [associativity] =(BA’+B’C+A’C)+BC’ [commutativity] =BA’+B’C+BC’ [consensus]...
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