Question

Design a digital circuit for output ‘e’ for the seven segment display for all possible inputs.

Inputs: ABCD

a

f b

g   

e c

d

A) Derive a truth table

B) Design using K-Map technique, a minimum AND-OR gate network for this system. Draw the resulting digital circuit diagram

Answer 1

A seven segment display is a arrangement of LED in H shape The truth table of a seven segment led is created with combination of inputs for each decimal number and is shown below

	input				output
Decimal number	A	B	C	D	a	b	c	d	e	f	g
0	0	0	0	0	x	x	x	x	x	x
1	0	0	0	1		x	x
2	0	0	1	0	x	x		x	x		x
3	0	0	1	1	x	x	x	x			x
4	0	1	0	0		x	x			x	x
5	0	1	0	1	x		x	x		x	x
6	0	1	1	0	x		x	x	x	x	x
7	0	1	1	1	x	x	x
8	1	0	0	0	x	x	x	x	x	x	x
9	1	0	0	1	x	x	x			x	x

Now we find the Boolean expression for each of output function

a=f(A,B,C,D)=m(0,2,3,5,7,8,9)

b=f(A,B,C,D)=m(0,1,2,3,4,7,8,9)

c=f(A,B,C,D)=m(0,1,3,4,5,6,7,8,9)

d=f(A,B,C,D)=m(0,2,3,5,6,8)

e=f(A,B,C,D)=m(0,2,6 8)

f=f(A,B,C,D)=m(0,4,5,6,8,9)

g=f(A,B,C,D)=m(2,3,4,5,6,8,9)

next we draw the K map for each of output and simplify it

Next we draw the circuit using logic gates where A<B<C<D is input and output are a,b,c, d,e,f,g,