Boolean functions

what are boolean functions
boolaen variables.

1. LECTURE -8
BOOLEANFUNCTIONS
&
ALGEBRAIC MANIPULATIONS

2. BOOLEAN FUNCTIONS
■EXPRESSIONSthat contain:
–Binary Variables
■Values = 0,1
–Binary Operators
■OR, AND, NOT
–Parenthesis *Optional
–Equal Sign
F = xy’ + x’z

3. F = xy’ + x’y
x y x’y’x.y’x’.yF
0 0 1 1 0 0 0
0 1 1 0 0 1 1
1 0 0 1 1 0 1
1 1 0 0 0 0 0

4. SIMPLIFICATION USING BOOLEAN
ALGEBRA
■Simplification of Boolean Expressions may be done using:
–Laws / Postulates
–Rules
–Theorems

5. Advantage of Simplification
■Fewer Variables
■Simpler Circuit

6. EXAMPLE
F = A.B + A.(B+C) + B.(B+C)
Total No. of Gates= 5
A
B
C
A.B
A.(B+C)
B.(B+C)
F

7. Simplification of
F = A.B + A.(B+C) + B.(B+C)
F = A.B + A.(B+C) + B.(B+C)
= AB + AB + AC + BB + BC
= AB+ AC +B+ BC
= AB + AC + B (1 + C)
= AB + AC +B (1)
= AB + AC +B
= AB + B+ AC
= B (A + 1)+ AC
= B (1)+ AC
=B + AC

8. SIMPLIFIED OUTPUT:
F = B + AC
Circuit Diagram
A
B
C
A.C
B
F = B + AC
Total No. of Gates = 2

9. MORE EXAMPLES
1.x + x’y
2.x (x’+y)
3.x’y’z + x’yz + xy’
4.xy + x’z + yz
5.(x+y).(x’+z).(y+z)
6.y (wz’ +wz) + xy

10. SOLUTIONS TO EXAMPLES
1.x+y
2.xy
3.x’z+xy’
4.xy+x’z
5.x’y+xz
6.y (x+w)

11. CIRCUIT DIAGRAMS
HOMEWORK:
Draw the Circuit Diagrams of the
examples