Use Quine Mc-Cluskey method to simplify the logic function as given below. $F(A,B,C,D,E) = \sum m(0,1,8,10,11,12,20,21,30)+d(14,19)$ Realize the above using NAND gates .

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written 9.5 years ago by

teamques10 ★ 70k

Grouping the minterms based on number of 1’s

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Now, Grouping the minterms of the adjacent groups based on the criteria of only one bit change.

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Now, Grouping the minterms of the adjacent groups based on the criteria of two bit change.

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PI table: Write down all the terms with value of checked = No from all the 3 tables

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$$F=\underline{ABCD}+\underline{A}B\underline{C}D+A\underline{B}C\underline{D}+BCD\underline{E}+\underline{A}B\underline{E}$$

Let ,$P = \underline{ABCD}, Q=\underline{A}B\underline{C}D, R = A\underline{B}C\underline{D}, S= BCD\underline{E} \ \ and \ \ T= \underline{A}B\underline{E}$

Therefore, F = P+Q+R+S+T

$\underline{\underline{F}}=\underline{\underline{P+Q+R+S+T}}...........\text{Double Inversion} \\ F=\underline{\underline{P}.\underline{Q}.\underline{R}.\underline{S}.\underline{T}}…..\text{De Morgan’s theorem} \\ F=\underline{\underline{\underline{ABCD}}.\underline{\underline{A}B\underline{C}D}.\underline{A\underline{B}C\underline{D}}.\underline{BCD\underline{E}}.\underline{\underline{A}B\underline{E}}}$

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