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Binary Numbers 1s_complement 2s_complement Binary Subtraction Binary Sub. Ex's Sign_magnitude SignM EX Gray Coding BCD coding Digital gates NAND NOR & XNOR Theorems Boolean Functions BFunc Examples Minterm Maxterm Sum of Minterms Prdt of Maxterms 2 var K-map 3 var K-map 4 var K-map 5 var K-map Prime Implicant PI example K-map Ex's KMap minimization 2 var EX

Answers derived using Boolean Theorems and postulates.

Example 2:-

F = x + x’y

From Postulate P8

= (x + x’)(x + y)

From Postulate P3

F = x + y . Answer

Example 3:-

F = (x + y)(x +y’)

From Postulate P8

= x + yy’

From Postulate P4

= x .ans

Example 4:-

F = xy + x’z + yz

From Postulate P3

= xy + x’z + xyz + x’yz

= xy(1 + z) + x’z(1 + y)

= xy + x’z .ans

Example 5:-

F = xyz + x’y + xyz’

= xyz + x’yz + x’yz’ + xyz’

= yz + yz’

= y

Simplify following Boolean Functions:

1. F = xy + x’y + xy’

2. F = x + x’y

3. F = (x + y)(x +y’)

4. F = xy + x’z + yz

5. F = xyz + x’y + xyz’

Example 1:-

F = xy + x’y + xy’

From Theorem T1

= xy + xy + x’y + xy’

= y(x + x’) + x(y + y’)

From Postulate P3

= y + x . Answer

Access previous topic for details on Boolean Functions, equivalent truth table and gate level implementation. Examples are discussed next.

Exercise :-

Boolean Functions.
Minterm Maxterm.
Interview Questions. Main, FPGA, Digital Fundamentals

Guide to Graduate studies in USA.

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