## Related questions with answers

Find a minimum two-level, multiple-output AND-OR gate circuit to realize these functions (eight gates minimum).

$\begin{array}{l} f_{1}(a, b, c, d)=\Sigma m(10,11,12,15)+\Sigma d(4,8,14) \\ f_{2}(a, b, c, d)=\Sigma m(0,4,8,9)+\Sigma d(1,10,12) \\ f_{3}(a, b, c, d)=\Sigma m(4,11,13,14,15)+\Sigma d(5,9,12) \end{array}$

Solution

VerifiedGiven:

$\begin{align*} f_1(a,b,c,d)&=\sum m(10,11,12,15)+\sum d(4,8,14) \\ f_2(a,b,c,d)&=\sum m(0,4,8,9)+\sum d(1,10,12) \\ f_3(a,b,c,d)&=\sum m(4,11,13,14,15)+\sum d(5,9,12) \end{align*}$

$\text{\underline{Step 1}}$: For each $i$ mentioned in $\sum m(..., i, ...)$, we add a 1 in the cell corresponding to $m_i$ (index is given in a corner of each cell).

For each $i$ mentioned in $\sum d(..., i, ...)$, we add an $X$ in the cell corresponding to $m_i$.

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