Re: Module 1 - Discussion Topic 1 - Karnaugh Maps
Author: Theresa Lynn Ford

This includes SOP and POS. The attachment contains a dynamic circuit diagram in Excel. I realize this is beyond the scope of the assignment but I wanted to make sure I understood the topic.

 abcd output 0000 1 0001 0 0010 1 0011 0 0100 0 0101 1 0110 0 0111 1 1000 1 1001 0 1010 1 1011 0 1100 0 1101 x 1110 x 1111 x
 c 00 01 11 10 00 1 0 0 1 01 0 1 1 0 b a 11 0 x x x 10 1 0 0 1 d
 SOP Solution F = b'd' + bd POS Solution F' = b'd + bd' F = (b'+ d ) * (b + d')
```F = a'b'c'd' + a'b'cd' + a'bc'd + a'bcd + ab'c'd' + ab'cd'
= a'(b'c'd' + b'cd' + bc'd + bcd)     + a(b'c'd' + b'cd')
= a'(b'(c'd' + cd') + b(c'd + cd))    + a(b'(c'd' + cd'))
= a'(b'(d'(c' + c)) + b(d(c' + c)))   + a(b'(d'(c' + c)))
= a'b'd'            + bd              + ab'd'
= a'b'd'            + ab'd'           + bd
= b'(a'd' + ad')                      + bd
= b'(d'(a' + a))                      + bd
= b'd'                                + bd
```

* POS is wrong above:
F' = b'd + bd'
F = (b'd)'(bd')'
F = (b + d')(b' + d)