UNIT 1: Modeling Digital Circuits
Module 1 : Functional Modeling
TOPIC : Truth tables and Primitive
Cubes
Truth table
Representation of the function in terms of rows and
columns.
◦ The rows represent inputs and the corresponding outputs.
◦ Columns are input and output variables.
 It is the simplest way to represent a circuit.
 In Boolean arithmetic, the possible values are 0 and 1. So for
an n-input gate,
number of possible outcomes = 2n
 The inputs are given in an increment of 1 from 0 to 2n-1 in
Boolean form.

How the truth table is
constructed??
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Assume there are n inputs (x1,x2,…,xn)
There are 2n different possible input vectors.
Start the first row with (0,0,…,0) as inputs.
Write the corresponding outputs in the same row.
Increment the input vector value by 1 in the subsequent rows and
enter the outputs.
Follow this till the last 2n th vector (1,1,…,1) is reached
Example of a truth table
A
B
C
Out
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
Out = AB’C + A’BC’
Primitive Cubes
Primitive cubes are compressed form of truth tables.
 Observe the truth table of AND gate given below:


A
B
Out(AN
D)
0
0
0
0
1
0
1
0
0
1
1
1
Have a look at the first two inputs:
A=0, then out=0 irrespective of the second input B.
For these two input vectors, we call the B input as don’t
care.
Primitive cube examples
A
B
Out(AN
D)
A
B
Out(AN
D)
0
0
0
0
X
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
Truth table of AND gate
Primitive cube of AND gate
X is don’t care
A
B
Out(NOR)
A
B
Out(NO
R)
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
X
0
Truth table of NOR gate
Primitive cube of NOR gate