Ch 4. Combinational Logic Design Principles Combinational Logic Circuit –Outputs depend only on its current inputs –No feedback loop Sequential Logic Circuit –Outputs depend on its current inputs and present states –Feedback loop

4.1 Switching Algebra

‘+’ : ‘OR’

& are obvious (by perfect induction) is identical to the distributive law for integers and reals Switching-algebra theorems

NAND DeMorgan’s Th.

NOR DeMorgan’s Th.

Black box Representation with Truth table Active Low

Black box Representation with Truth table

Duality PositiveNegative

Function with 3 input X, Y, Z

DeMorgan’s Th.

4.2 Combinational-Circuit Analysis

F(X, Y, Z)

Three-level without considering inverter

“Add-out” to obtain a product of sums by T8’ Sum of products Product of sums (Figure 4-12) (Figure 4-13) Same

4.3 Combinational-Circuit Synthesis Prime number detector

NAND NOR

4.4 Timing Hazards Unwanted Output Static-1 Hazard : Momentary output ‘0’ to occur during a transition in the differing input variable Static-0 Hazard : Momentary output ‘1’ to occur during a transition in the differing input variable

Unwanted Output