So according to question our objective is to make a function X that output high when an unused codeword occurs in input and for all correct BCD inputs it outputs low.
So we will make truth table Now using 4 inputs B8, B4, B2, B1, and output X. We will mark all non BCD codeword in output as 1 and other inputs as 0. All codeword from 0-9 is marked as 0 in output and 10-15 as 1.
Truth Table:
B8 | B4 | B2 | B1 | X |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 |
Let us make K-map for this truth table
We have 6 minterms in X given below
So finally we have the expression for X
Logic Circuit for expression is given below
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