homework_7_ece15a2011

homework_7_ece15a2011 - The input combination(x,y,z,w...

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Homework #7 February 16, 2011 1 Homework #7 due February 28 at noon ECE 15a Winter 2011 1. (15p) Design a combinational circuit with three inputs, x,y, and z, and three outputs: A, B, and C. When the binary input is 0, 2, 4 or 6, the binary output is one less than the input. When the binary input is 1, 3, 5 or 7, the binary output is one greater than the input. 2. (10p) A majority circuit is a combinational circuit whose output is equal to 1 if the input variables have more 1’s than 0’s. The output is 0 otherwise. Design a 6-input majority circuit. 3. (10p) Design an 8-bit combinational circuit 2’s complementer. (The output generates the 2’s comple- ment of the binary number presented at the input.) Show that the circuit can be constructed using exclusive- OR gates. 4. (5p) Consider the following circuit:
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Unformatted text preview: The input combination (x,y,z,w) = (0,0,1,1) never occurs. Simplify the circuit such that the simplified and the old circuit produce the same output values for those input combinations that may occur. (5p)5. Construct a 4-to-16 line decoder with five 2-to-4 line decoders with enable. (5p) 6. A combinational circuit is defined by the following three Boolean functions: F1= x’y’z’+xz F2=x’yz’+yz’ F3=x’y’z+xy Design the circuit with a decoder and external gates. (5p) 7. Construct a 16x1 multiplexer with two 8x1 and one 2x1 multiplexers. Use block diagrams. (5p) 8. Implement the following Boolean function using a multiplexer of the smallest possible size. F(A,B,C,D) = (1,3,5,7,9,10,13,14) x y z w a b c F d...
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