Re: Module 1 - Discussion Topic 1

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)