1. Create and document the following series of combinational logic circuits.

a) A two – input decoder

i1 i2 d3 d2 d1 d0

0 0 0 0 0 1

0 1 0 0 1 0

1 0 0 1 0 0

1 1 1 0 0 0

b) A three – input decoder

i2 i1 i0 d7 d6 d5 d4 d3 d2 d1 d0

0 0 0 0 0 0 0 0 0 0 1

0 0 1 0 0 0 0 0 0 1 0

0 1 0 0 0 0 0 0 1 0 0

0 1 1 0 0 0 0 1 0 0 0

1 0 0 0 0 0 1 0 0 0 0

1 0 1 0 0 1 0 0 0 0 0

1 1 0 0 1 0 0 0 0 0 0

1 1 1 1 0 0 0 0 0 0 0

c) A 2-to-1 Mux

S0 Y

0 I0

1 I1

Y = S0 I0 + So I1

d) A 4-to-1 MUX

S1 S0 Y

0 0 I0

0 1 I1

1 0 I2

1 1 I3

Y = S1 S0 I0 + S1 S0 I1 + S1 SO I2 + S1 S0 I3

e) A 2-bit Adder

X Y Sum Carry

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1

S = ( X * Y + X * Y )

C = X * Y

f) A 4-bit Adder

Sum = A B C + A B C + A B C + A B C

Carry = A B C + A B C + A B C + A B C

= AB + AC + BC

g) A 8-bit Adder

In this we saw that for a combinational circuit of n input variables, there are 2n possible input combinations. We then came across decoder, multiplexer and adder. A decoder is basically a combinational circuit that converts binary information from the n coded inputs to a maximum of 2n unique outputs. Whereas, a multiplexer is a combinational circuit that receives binary data from one of the 2n input data lines and directs it to a single output line. Then we learnt about the two types of adder : Half adder and Full adder. A combinational circuit that performs the addition of two bits is called a half adder. A full adder is a three input and two output combinational circuit.