Question

a	b	c	d	f
0	0	0	0	0
0	0	0	1	0
0	0	1	0	0
0	0	1	1	0
0	1	0	0	1
0	1	0	1	1
0	1	1	0	1
0	1	1	1	1
1	0	0	0	0
1	0	0	1	1
1	0	1	0	1
1	0	1	1	1
1	1	0	0	0
1	1	0	1	1
1	1	1	0	1
1	1	1	1	0

a)Implement f using one 4-to-16 decoder and a minimal number of gates.

b) Implement f using two 2-to-8 decoders, one 4-to-1 multiplexer, and a minimal number of gates.

Answer 1

Truth Table:

S.NO	a	b	c	d	f
0	0	0	0	0	0
1	0	0	0	1	0
2	0	0	1	0	0
3	0	0	1	1	0
4	0	1	0	0	1
5	0	1	0	1	1
6	0	1	1	0	1
7	0	1	1	1	1
8	1	0	0	0	0
9	1	0	0	1	1
10	1	0	1	0	1
11	1	0	1	1	1
12	1	1	0	0	0
13	1	1	0	1	1
14	1	1	1	0	1
15	1	1	1	1	0

a) From the above truth table

Given Function is

f (a, b, c, d) =m (4, 5, 6, 7, 9, 10, 11, 13, 14)

Decoder: Definition: A decoder is a combinational circuit that has n data inputs and 2ⁿ Outputs.In given data it has 4 data inputs so 2⁴ Outputs

2⁴ Outputs = 2x2x2x2 = 16 Outputs

Using 4-to-16 Decoders:

Given Function is

f (a, b, c, d) =m (4, 5, 6, 7, 9, 10, 11, 13, 14)

Explanation:

Here in the above function we have min terms m4,m5,m6,m7,m9, m10,m11,m13 & m14. So combine output contains these min terms & Joined to OR gate.

b) Decoder: Definition: A decoder is a combinational circuit that has n data inputs and 2ⁿ Outputs.In given data it has 3 data inputs so 2³ Outputs

2³ Outputs = 2x2x2 = 8 Outputs

Using 3-to-8 Decoders:

Given Function is

f (a, b, c, d) =m (4, 5, 6, 7, 9, 10, 11, 13, 14)

Using 3 to 8 Decoder:

Explanation:

Here in the above function we have min terms m4,m5,m6,m7,m9, m10,m11,m13 & m14. So combine output contains these min terms & Joined to OR gate.

Using 4-to-1 Multiplexer:

Explanation:

Here in the above function we have min terms m4,m5,m6,m7,m9, m10,m11,m13 & m14. So combine output contains these min terms & Joined to OR gate.