Digital electronics lab-K map minimisation

1. Design a circuit which generates the square of 3 bit BCD number.

Sol: The Square of a 3 bit BCD number is a 6 bit number. So first write the truth table.

          INPUT                                                                                         OUTPUT

A	B	C		S6	S5	S4	S3	S2	S1
0	0	0		0	0	0	0	0	0
0	0	1		0	0	0	0	0	1
0	1	0		0	0	0	1	0	0
0	1	1		0	0	1	0	0	1
1	0	0		0	1	0	0	0	0
1	0	1		0	1	1	0	0	1
1	1	0		1	0	0	1	0	0
1	1	1		1	1	0	0	0	1

By minimal expressions are given as follows (you can use K map to do this)

S1=C

S2=0

S3=BC*

S4=C (A⊕B)

S5=A (B*+C)

S6=AB

[“*” represents complement]

Using these equations logic diagrams can be drawn.