20
Representations of Boolean Functions
Readings: 2.5,2.5.2-2.10.3
Boolean Function:
F = X + YZ
Truth Table:
X
Y
Z
F
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
Circuit Diagram:
21
Why Boolean Algebra/Logic Minimization?
Logic Minimization: reduce complexity of the gate level implementation
•
reduce number of literals (gate inputs)
•
reduce number of gates
•
reduce number of levels of gates
fewer inputs implies faster gates in some technologies
fan-ins (number of gate inputs) are limited in some technologies
fewer levels of gates implies reduced signal propagation delays
number of gates (or gate packages) influences manufacturing costs

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
22
Basic Boolean Identities:
X + 0 =
X * 1 =
X + 1 =
X * 0 =
X + X =
X * X =
X + X =
X * X =
X =
23
Basic Laws
Commutative Law:
X + Y = Y + X
XY = YX
Associative Law:
X+(Y+Z) = (X+Y)+Z
X(YZ)=(XY)Z
Distributive Law:
X(Y+Z) = XY + XZ
X+YZ = (X+Y)(X+Z)