Page 34 - Digital Electronics by harish

1.4.2 Implementation of logic functions using gates

The following table shows the various logic equations and their equivalent gates.

Logic equation Name of the gate Symbol

NOT

A + B OR

A . B AND

+ NOR

. NAND

. B + A . EX-OR

. + . EX-NOR

The given logic function can be realized using gates as per the above table.

Different forms of logic functions:

There are two different forms of logic functions. They are,

1. Sum-of-products form (or) Minterm form - SOP
2. Product-of-sums form (or) Maxterm form - POS

Consider the following two logic functions.

Y = ( . B) + (A .) + ( . C) …………. 1
Y = (A + B + C) . (+ ) …………. 2

The first equation has three terms. Each term is a product term. The logic function is the sum
of the product terms. This function is said to be in Sum-of-products form (or) Min term form.
Similarly, the second equation has two terms. Each term is a sum term. The logic function is
the product for the sum terms. Hence, this function is said to be in Product-of-sums form (or)
Max term form.

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