Module 5: Digital Techniques and Electronic Instrument Systems

5.5 Logic Circuits

Digital Systems Hardware Design Flow

1. System Level Design 2. RTL Design

3. Physical Design

4. Layout synthesis

5. The final circuit

Gates AND - OR - NOT

x y f

0 0 0

0 1 0

1 0 0

1 1 1

x f

0 1

1 0

AND NOT (Inverter)

x y f

0 0 0

0 1 1

1 0 1

1 1 1

OR

f = x + yf = xy

Gate NAND

x y f = xy

0 0 0

0 1 0

1 0 0

1 1 1

AND

x y f = xy

0 0 1

0 1 1

1 0 1

1 1 0

NAND

Gate NOR

x y f = x+y

0 0 1

0 1 0

1 0 0

1 1 0

NOR

x y f = x+y

0 0 0

0 1 1

1 0 1

1 1 1

OR

Analyzing a digital circuit (1/2)

x y f = xy + xy

0 0 0

0 1 1

1 0 1

1 1 0

Gate EXOR

x y f = xy + xy

0 0 0

0 1 1

1 0 1

1 1 0

Analyzing a digital circuit (2/2)

x y S C

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1

Half-adder: Adds two bits.

Full Adder

x y Cn-1 S C

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

Fan-In and Fan-out Fan-In: the number of digital inputs of a

digital circuit. Fan-Out: the number of digital outputs of a

digital circuit.

From a Digital Circuit to the Truth Table

1st way: Apply all possible

inputs to the circuit and fill the Truth Table.

2nd way: Find the

Boolean expression and determine the output for each Truth Table record.

From the Truth Table to the Digital Circuit

x y z f

0 0 0 1

0 0 1 1

0 1 0 0

0 1 1 0

1 0 0 1

1 0 1 1

1 1 0 1

1 1 1 0

x/ yz 00 01 11 10

0 1 1 0 0

1 1 1 0 1

Which variables do not vary in this team? y, which is “0”.

Which variables do not vary in this team? All

y΄

So: f = xyz΄ + y΄

xyz΄