Question

2. Design a combinational circuit with three inputs, x,y, and z, and three outputs, A,B, and C. When the binary input is 0,1,2, or 3 , the binary output is one greater than the input. When the binary input is 4,5,6, or 7 , the binary output is one less than the input.

Answer 1

The given truth table describes the relationship between inputs x, y, z and outputs A, B, C based on binary input ranges 0-3 and 4-7. Using Boolean algebra or Karnaugh maps, derive simplified expressions for A, B, and C. Then implement the combinational circuit using logic gates to fulfill the specified conditions for input and output relationships.

To design this combinational circuit, we'll create a truth table based on the given conditions for inputs x, y, and z, and outputs A, B, and C.

Step 1: Construct a Truth Table

Inputs x, y, z can represent the 3-bit binary number (x2^2 + y2^1 + z2^0).

Define the outputs A, B, C based on the given conditions.

x y z Input A B C

0 0 0 0 1 0 0

0 0 1 1 0 1 0

0 1 0 2 0 0 1

0 1 1 3 0 0 0

1 0 0 4 0 0 1

1 0 1 5 0 1 0

1 1 0 6 1 0 0

1 1 1 7 0 0 0

Step 2: Design Logic Circuits

Use Karnaugh maps or Boolean algebra to derive simplified expressions for A, B, and C based on the truth table.

Step 3: Implement the Circuit

Using logic gates (AND, OR, NOT, etc.), construct the circuit based on the derived expressions for A, B, and C.

The resulting combinational circuit will take inputs x, y, and z and generate outputs A, B, and C according to the defined conditions for input ranges 0-3 and 4-7.