boolean algebra: simplify $ a* b d + \tilde a \tilde cd + b \tilde c* d$

Question

Simplify the following function(algebraically): $$y = a*b*d + \tilde a *\tilde c*d + b *\tilde c *d$$

the solution is: $$a*b*d + \tilde a * \tilde c * d$$ which i checked via karnaugh and also wolfram.

my "solution" so far: $b*d*(a + \tilde c) + (\tilde a * \tilde c * d)$ there should be a rule that should eliminate the $\tilde c$ inside the $(a +\tilde c)$ term. Does anybody know how to do it?

So you have identified AND, OR and NOT, but what does $(abd)$ mean? $(abd)$? — Dilip Sarwate, Jul 16 '13 at 19:26
For some basic information about writing math at this site see e.g. here, here, here and here. — Cortizol, Jul 16 '13 at 19:45

score 1 · Accepted Answer · answered Jul 16 '13 at 19:52

Hint: write $$b*\tilde c*d = a*b*\tilde c*d + \tilde a*b*\tilde c*d$$ and then see if you can absorb

$a*b*\tilde c*d$ into $a*b*d$
and $\tilde a*b*\tilde c*d$ into $\tilde a*\tilde c*d$

using $x+ x*y = x*(1+y) = x*1 = x$ for suitable choices of $x$ and $y$.

boolean algebra: simplify $ a* b *d + \tilde a *\tilde c*d + b* \tilde c* d$

1 Answers1

boolean algebra: simplify $ a* b d + \tilde a \tilde cd + b \tilde c* d$