Question: in this problem you will design a combinational circuit that...
Question details
In this problem you will design a combinational circuit that identifies the largest prime factor of the numbers between 2 and 15 (inclusive). The input is a 4-bit number B = (b_{3},b_{2},b_{1},b_{0}) and the output is a 4-bit number N = (n_{3},n_{2},n_{1},n_{0}) The values 0 and 1 (inputs 0000 and 0001) are don't cares because they have no prime factor. For your reference, below is a table giving the largest prime factor of the numbers between 2 and 15.
B | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
N | - | - | 2 | 3 | 2 | 5 | 3 | 7 | 2 | 3 | 5 | 11 | 3 | 13 | 7 | 5 |
- (2 points) Fill in a truth table for the outputs (n_{3},n_{2},n_{1},n_{0}) as a function of the inputs (b_{3},b_{2},b_{1},b_{0}) for all 16 possible input values.
- (9 points) Using Karnaugh maps obtain minimal SOP expressions for each of the 4 outputs.