## Related questions with answers

Find a minimum two-level OR-AND circuit to simultaneously realize $F_{1}(a, b, c, d)=\Sigma m(2,3,8,9,14,15)$ $F_{2}(a, b, c, d)=\Sigma m(0,1,5,8,9,14,15)$ (minimum solution has eight gates)

Solutions

VerifiedGiven:

$\begin{align*} F_1(a,b,c,d)&=\sum m(2,3,8,9,14,15) \\ F_2(a,b,c,d)&=\sum m(0,1,5,8,9,14,15) \end{align*}$

$\text{\underline{Step 1}}$: 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).

We add a 0 to all remaining cells.

a)

Let us first find the expression for the function F

$\begin{align*} F = \sum m(2,3,8,9,14,15) \tag{\color{#c34632}{given}}\\ \end{align*}$

We will be using the kmap as shown in figure below to derive the expression for F

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