I am working on a problem where I have to draw a logic circuit using no more than 2 Nor gates. The function F(A, B, C, D) = Σ(2,4,10,12,14) with don't care conditions Σ(0,1,5,8). After drawing the k-map and working through the functions, I am ready to say that it can't be done.
| ab\cd | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 00 | x | x | 0 | 1 |
| 01 | 1 | x | 0 | 0 |
| 11 | 1 | 0 | 0 | 1 |
| 10 | x | 0 | 0 | 1 |
C'D' + ACD' + A'B'CD'
D'(C'+AC+A'CB')
D'(C'(A+A')+AC+A'B'C)
D'(AC'+AC+A'C'+A'B'C)
D'(A+A'C'+A'B'C)
D'(A+A'(C'+B'C)
ChatGPT is telling me that C'+B'C is 1, so the entire function boils down to D', which I know isn't true. If I try to choose the largest possible groups from the kmap, I get C'D'+ ACD' + A'B'D', which comes down to D'(C'+B'+A)
I also know that 2 nor gates can handle a maximum of 3 inputs. Am I right in saying there is no solution?
From the Karnaugh map:
F = B'D' + C'D' + AD'
This can be rewritten:
F = (B' + C' + A) D'
Finally:
F = ((B' + C' + A)' + D)'
Disregarding the inverted inputs, this is a circuit with two NOR gates.