Chapter 1: Q8E (page 2)
Implement the four-input odd-parity function with AND and OR gates using bubbled inputs and outputs.
Short Answer
Use 8 AND gates for the input combinations 0000, 0011, 0101, 0110, 1001, 1010, 1100, and 1111. The implementation of the four-input odd-parity function can be performed with OR operation on the output of these.
Step by step solution
Identify the truth table for the four-input odd-parity function
The parity bit is one if there are even numbers of 1s in the input. Otherwise, it is zero. The truth table is given below:
Data bit 4 (D4) | Data bit 3 (D3) | Data bit 2 (D2) | Data bit 1 (D1) | Parity bit |
0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 1 |
Implementation of odd-parity function using AND and OR gates
The parity bit is 1 for the following inputs:
0000, 0011, 0101, 0110, 1001, 1010, 1100, and 1111.
The odd-parity function can be implemented by having OR operation on all these combinations of inputs as shown below:
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