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State DeMorgan's Laws.
written 9.5 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 9.5 years ago

Mumbai University > COMPS > Sem 3 > Digital Logic Design and Analysis

Marks: 2 M

Year: May 2015
digital logic design
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written 9.5 years ago by gravatar for teamques10 teamques10 ★ 70k

DeMorgan’s Theorms

DeMorgan’s Theorem is an important part of Boolean Algebra.

Theorem 1: $\overline{AB}=\overline{A}+\overline{B}$

The complements of product is equal to the sum of the complements.

-As shown in Truth Table

A B $\overline{AB}$ $\overline{A}+\overline{B}$
0 0 1 1
0 1 1 1
1 0 1 1
1 1 0 0

Theorem 2: $\overline{A+B}=\overline{A}\bullet\overline{B}$

The complement of sum is equal to the produce of the complements

-As shown in Truth Table

Minterm Binary Representation
$M_1$ 0 0 0 1,√
$M_3$ 0 0 1 1,√
$M_7$ 1 0 0 1,√
$M_9$ 1 0 1 0,√
$M_{10}$ 0 1 1 1,√
$M_{11}$ 1 0 1 1,√
$M_{13}$ 1 1 0 1,√
$M_{15}$ 1 1 1 1,√
A B $\overline{AB}$ $\overline{A}+\overline{B}$
0 0 1 1
0 1 0 0
1 0 0 0
1 1 0 0
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