Eee hw 3

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Electrical Engineering

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Jun 14, 2024

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Chapter 5, problem 7: (10 pts) Consider the following circuit with an active high output decoder. Draw a truth table for X and Y in terms of a, b. and c. X=SUM m(3, 5, 6, 7) Y= SUM m(1, 3, 5, 7) A B C X Y 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 Chapter 5, problem 8: (15 pts) We wish to design a decoder, with three inputs, x, y, z, and eight active high outputs, labeled 0, 1, 2, 3, 4, 5, 6, 7. There is no enable input required. (For example, if xyz = 011, then output 3 would be 1 and all other outputs would be 0.) The only building block is a two-input, four output decoder (with an active high enable). x=0 X Y Z 0 1 2 3 4 5 6 7 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 x=1 X Y Z 0 1 2 3 4 5 6 7 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 Chapter 5, problem 9: (10 pts) We want to implement a full adder: we’ll call the inputs a, b, and c and the outputs s and c out . As always, the adder is described by the following equations: s(a, b, c) = m(1, 2, 4, 7) c out (a, b, c) = m(3, 5, 6, 7) To implement all this, all we have available are two decoders (as shown below) and two OR gates. Inputs a and b are available both uncomplemented and complemented; c is available only uncomplemented. Show a block diagram for this system. Be sure to label all of the inputs to the decoders. Chapter 5, problem 12: (10 pts) Implement the function f(x, y, z) = m(0, 1, 3, 4, 7) using 2:1 multiplexers. Chapter 5, problem 14: (5 pts) The following circuit includes a multiplexer with select inputs A and B, and data inputs W, X, Y, and Z. Write an algebraic equation for F. F = A'B'W+A'BX+AB'Y+ ABZ
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