1. Module 5: Digital Techniques and
Electronic Instrument Systems
5.5 Logic Circuits

2. Digital Systems Hardware Design Flow
 1. System Level Design  2. RTL Design
 3. Physical Design
 4. Layout synthesis
 5. The final
circuit

3. 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

4. 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

5. 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

6. Analyzing a digital circuit (1/2)
x y f = xy + xy
0 0 0
0 1 1
1 0 1
1 1 0

7. Gate EXOR
x y f = xy + xy
0 0 0
0 1 1
1 0 1
1 1 0

8. 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.

9. 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

10. 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.

11. 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.

12. 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΄