TOPIC : Truth tables and TOPIC : Truth tables and Primitive CubesPrimitive Cubes

UNIT 1: Modeling Digital Circuits

Module 1 : Functional Modeling

Truth tableTruth 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 How the truth table is constructed??constructed??

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 tableExample 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 CubesPrimitive Cubes Primitive cubes are compressed form of truth

tables. Observe the truth table of AND gate given below:

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.

A B Out(AND)

0 0 0

0 1 0

1 0 0

1 1 1

Primitive cube examplesPrimitive cube examplesA B Out(AN

D)

0 0 0

0 1 0

1 0 0

1 1 1

A B Out(AND)

0 X 0

1 0 0

1 1 1

Truth table of AND gatePrimitive cube of AND gate

A B Out(NOR)

0 0 1

0 1 0

1 0 0

1 1 0

A B Out(NOR)

0 0 1

0 1 0

1 X 0

X is don’t care

Truth table of NOR gatePrimitive cube of NOR gate