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Design a circuit with three inputs x,y and z representing the bits in a binary number,...

Design a circuit with three inputs x,y and z representing the bits in a binary number, and three outputs (a,b, and c) also representing bits in a binary number. When the input is 0,1,6, or 7, the binary output will be the complement of the input. When the binary input 2,3,4, or 5 the output is the input shifted left with rotate. For example: 3 = 011₂ outputs 110; 4 = 100₂ outputs 001.) Show truth table, computation, simplification and final circuit.

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Answer #1

For a circuit with three inputs x,y and z representing the bits in a binary number, and three outputs (a,b, and c) also representing bits in a binary number. With the given information we can design a Truth table:

INPUT OUTPUT
x y z a b c
0 0 0 0 1 1 1
1 0 0 1 1 1 0
2 0 1 0 0 1 0
3 0 1 1 1 1 0
4 1 0 0 0 0 1
5 1 0 1 1 0 1
6 1 1 0 0 0 1
7 1 1 1 0 0 0

From the above Truth table we can Compute the K-maps fo output a,b and c and simplify(if can).

We have the boolean expression of the outputs:

Now Implementing the expressions in circuit, using required logic gates:

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