I have some homework I can't seem to figure out. The assignment causing problems is devided into two parts; The first is to determine the inverse formula for a given formula (so the S = F'). The second part asks me to simplify the answer to the first question. I've looked trough all materials I have, but I can't figure out what happens here:
(I've used the ' symbol as NOT)
The first formula is as follows:
(a·c·(b + d) + b·c'·d + a'·b)
Which, when i invert it without simplifying, results into:
(a' + c' + b'·d')·(b' + c + d')·(a + b')
So far, so good. However, when I look at the given solution for the second part of the assignment, I can't seem to figure out the logic behind the given steps.
(a' + c' + b'·d')·(b' + c + d')·(a + b') = (a'·b' + a·c' + b'·c' + a·b'·d' + b'·d')·(b' + c + d') = = (a'·b' + a·c' + b'·c' + b'·d')·(b' + c + d') = a'·b' + a·b'·c' + b'·c' + b'·d' + a'·b'·c + b'·c·d' + a'·b'·d' + a·c'·d' + b'·c'·d'+ b'·d' = = a'·b' + b'·c' + b'·d' + a·c'·d
Can anyone point me in the direction of what steps are taken here? Thanks in advance!