Digital LogicTU Board 2081
Explain design procedure of combinatorial circuits. Design a combinatorial 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…
10Explain design procedure of combinatorial circuits. Design a combinatorial 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 input is 4, 5, 6, or 7, the binary output is one less than the input.
Answer
Design procedure of a combinational circuit
- From the problem statement, decide the number of inputs and outputs and give each a name.
- Write the truth table relating inputs to outputs.
- Get the simplified Boolean expression for each output, using K-maps or Boolean algebra.
- Draw the logic diagram from the expressions.
- Verify the circuit against the truth table.
Design
Inputs x, y, z (x is the MSB); outputs A, B, C (A is the MSB). For inputs 0–3 the output is input + 1; for inputs 4–7 the output is input − 1.
| x y z | Decimal | Output | A B C |
|---|---|---|---|
| 0 0 0 | 0 | 1 | 0 0 1 |
| 0 0 1 | 1 | 2 | 0 1 0 |
| 0 1 0 | 2 | 3 | 0 1 1 |
| 0 1 1 | 3 | 4 | 1 0 0 |
| 1 0 0 | 4 | 3 | 0 1 1 |
| 1 0 1 | 5 | 4 | 1 0 0 |
| 1 1 0 | 6 | 5 | 1 0 1 |
| 1 1 1 | 7 | 6 | 1 1 0 |
Output A = Σm(3, 5, 6, 7). On the K-map the 1s pair up as (3,7), (5,7), (6,7):
A = xy + xz + yz
Output B = Σm(1, 2, 4, 7). These are exactly the inputs with an odd number of 1s, so no K-map grouping is possible and
B = x ⊕ y ⊕ z
Output C = Σm(0, 2, 4, 6). C is 1 whenever z = 0:
C = z′
Logic diagram: A uses three 2-input AND gates (xy, xz, yz) feeding a 3-input OR gate; B uses two XOR gates in series; C uses a single NOT gate on z.
Discussion
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