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ESE Electronics 2013 Paper 2: Official Paper

Option 2 : ABC̅D̅ + ABC̅D + ABCD̅ + ABCD + AB̅CD

CT 1: Current Affairs (Government Policies and Schemes)

54434

10 Questions
10 Marks
10 Mins

__Concept:__

**Canonical form**: Any Boolean function that expressed as a sum of minterms or as a product of max terms is said to be in its canonical form.

There are two types of canonical forms:

SOP:

Sum of products or sum of minterms

In SOP (sum of product) form, a minterm is represented by 1.

Example of SOP: XY + X’Y’

POS:

Product of sums or product of max terms

In POS (product of sum) form, a maxterm is represented by 0.

Example of POS: (X+Y) (X’+Y’)

__Calculation:__

F = AB + ACD

Converting the above logical expression in canonical form

F = AB(C + C̅)(D + D̅) + ACD(B + B̅)

= AB(CD̅ + CD + C̅D +C̅D̅) + ABCD + AB̅CD

= ABCD + ABCD̅ + ABC̅D + ABC̅D̅ + AB̅CD

= ABC̅D̅ + ABC̅D + ABCD̅ + AB̅CD