Introduction of combinational logic circuits and designing of half adder

1. Combinational Logic Circuits
T.V.Hyma Lakshmi

2. Contents
1. Introduction
2. Designing Steps
3. Example :Half Adder

3. Digital circuits are divided into
two types:
1. Combinational Logic Circuits
2. Sequential Logic Circuits

4. 1.Combinational Circuits 1.Sequential Circuits
2.Present Outputs depends on the present
inputs
3. It doesn’t consist of memory elements
4.It consists of Logic gates.
5. Adders, Subtractors, Multiplexers, etc.
2.Present Outputs depends on the present
inputs and past outputs
3. It consists of memory elements
4.It consists of Logic gates, Flip Flops and
Clock pulse
5. Flip Flops, Shift Registers, etc.
Comparison between Combinational Circuits and
Sequential Circuits
Combinational
Circuit
n inputs
m outputs
Combinational
Circuit
n inputs
m outputs
Memory
Element

5. Designing Steps: The design procedure for
combinational logic circuits starts with the problem
statement, ends at logic circuits diagram and comprises
the following steps:
1.Determine required number of inputs and outputs from the
specifications.
2.Derive the truth table for each of the outputs based on their
relationships to the input.
3.Simplify the boolean expression for each output. Use Karnaugh
Maps or Boolean algebra.
4.Draw a logic diagram that represents the simplified Boolean
expression. Verify the design by analysing or simulating the
circuit.

6. Half
Adder
A
B
S=Sum
C=C out
A B S C
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
0+0 = 0
0+1=1
1+0=1
1+1=10
1+1+1=11
2
1 Half adder is a combinational logic circuit with two inputs and two outputs. The
half adder circuit is designed to add two single bit binary numbers A and B. The
circuit has two outputs sum (s) and carry(C)

7. A B S C
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
1 𝐴 𝐵
A
B
0 1
0
1
1
1
Carry
AB
A
B 0 1
0
1
S=SUM
AB
2
3

8. 4
Sum=S=AB + AB =A + B
Carry=C= AB
A
B
A + B
AB

9. A B S C
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
1
1
A
B 0 1
0
1
S=SUM
AB
1 2
3
4
Half
Adder
A
B
S=Sum
C=C out
Sum=S=AB + AB =A + B
Carry=C= AB
A
B
S=A+ B
C=AB
1 𝐴 𝐵
A
B
0 1
0
1
Carry
AB
A
B 0 1
0
1
S=SUM

10. Thank you all

11. 1.Combinational Circuits 1.Sequential Circuits
2.Present Outputs depends on the present
inputs
3. It doesn’t consist of memory elements
4.It consists of Logic gates.
5. Adders, Subtractors, Multiplexers, etc.
2.Present Outputs depends on the present
inputs and past outputs
3. It consists of memory elements
4.It consists of Logic gates, Flip Flops and
Clock pulse
5. Flip Flops, Shift Registers, etc.
Comparison between Combinational Circuits and
Sequential Circuits
Combinational
Circuit
n inputs
m outputs
Combinational
Circuit
n inputs
m outputs
Memory
Element