2. INTRODUCTION
The digital system consists of two types of circuits, namely
Combinational circuits
Sequential circuits
Sequential Logic Circuit
Sequential logic circuit comprises both logic gates and the state of storage elements such
as flip-flops.
As a consequence, the output of a sequential circuit depends not only on present value of
inputs but also on the past state of inputs
3. Combinational Circuit
Combinational circuit consists of logic gates whose output at any time is determined from
the present combination of inputs.
The logic gate is the most basic building block of combinational logic.
The logical function performed by a combinational circuit is fully defined by a set of
Boolean expressions.
4. DESIGN PROCEDURE
Any combinational circuit can be designed by the following steps of design procedure.
1. The problem is stated.
2. Identify the input and output variables.
3. The input and output variables are assigned letter symbols.
4. Construction of a truth table to meet input -output requirements.
5. Writing Boolean expressions for various output variables in terms of input variables.
6. The simplified Boolean expression is obtained by any method of minimization—
algebraic method, Karnaugh map method, or tabulation method.
7. A logic diagram is realized from the simplified Boolean expression using logic gates.
5. PROBLEMS
1. Design a combinational circuit with three inputs and one output. The output is
1 when the binary value of the inputs is less than 3. The output is 0 otherwise.
Solution:
Truth Table:
x y z F
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0
7. 2. Design a combinational circuit with three inputs, x, y and z, and the three outputs, A, B, and
C. when the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. When
the binary input is 4, 5, 6, or 7, the binary output is one less than the input.
Solution:
Truth Table:
x y z A B C
0 0 0 0 0 1
0 0 1 0 1 0
0 1 0 0 1 1
0 1 1 1 0 0
1 0 0 0 1 1
1 0 1 1 0 0
1 1 0 1 0 1
1 1 1 1 1 0
8. K-map for output A:
The simplified expression from the map is: A= xz+ xy+ yz
LOGIC DIAGRAM
10. K-map for output B:
The simplified expression from the map is: B= x’y’z+ x’yz’+ xy’z’+ xyz
LOGIC DIAGRAM
11. K-map for output C:
The simplified expression from the map is: C=z’
LOGIC DIAGRAM
12. ARITHMETIC CIRCUITS
combinational logic building blocks that can be used to perform addition and subtraction
operations on binary numbers.
The basic building blocks that form the basis of all hardware used to perform the
arithmetic operations on binary numbers are half-adder, full adder, half-subtractor, full-
subtractor.
Half-Adder:
A half-adder is a combinational circuit that can be used to add two binary bits.
It has two inputs that represent the two bits to be added and two outputs, with one
producing the SUM output and the other producing the CARRY.
14. LOGIC DIAGRAM
FULL-ADDER
A full adder is a combinational circuit that forms the arithmetic sum of three input bits.
It consists of three inputs and two outputs.
Two of the input variables, represent the significant bits to be added.
The third input represents the carry from previous lower significant position.
