Description and working of Digital logic Circuits

1. Digital Logic Circuits
By :
Tamsil Shamsi

2. Half Adder
Logic Diagram
Truth Table
A half adder adds two one-bit binary
numbers A and B. It has two outputs, S
and C.
The simplest half-adder design, pictured
on the right, incorporates an XOR gate
for S and an AND gate for C. Half
adders cannot be used compositely,
given their incapacity for a carry-in bit.

3. Full Adder
A full adder adds binary numbers and
accounts for values carried in as well
as out. A one-bit full adder adds three
one-bit numbers, often written as A, B,
and Cin; A and B are the operands, and
Cin is a bit carried in.
A full adder can be constructed from
two half adders by connecting A and B
to the input of one half adder,
connecting the sum from that to an
input to the second adder, connecting
Cin to the other input and OR the two
carry outputs
Logic Diagram
Truth Table

4. SR Flip-Flop
Graphic Symbol
Truth Table
A SR flip-flop has three
inputs, S (for set), R (for
reset) and C (for clock). It
has an output Q.
The undefined condition
makes the SR flip-flop
difficult to manage and
therefore it is seldom used
in practice.

5. D Flip-Flop
Graphic Symbol
Truth Table
The D flip-flop is a slight
modification of the SR flip-
flop by inserting an inverter
between S and R and assigning
the symbol D to the single
input.
If D=1, the output goes to the
state 1, and if D=0, the output
of the flip flop goes to the 0
state.

6. JK Flip-Flop
Graphic Symbol
Truth Table
Inputs J and K behave like
inputs S and R. When inputs J
and K are both equal to 1, a
clock transition switches the
output of the flip-flop to their
complement state.

7. T Flip-Flop
Truth Table
Graphic Symbol
The T flip-flop is obtained
from a JK flip-flop when
inputs J and K are connected
to provide a single input
designated by T.
The flip-flop thus has only
two conditions.

8. Excitation Tables
During the design of
circuits, we need a table
that lists the required input
combinations for a given
change of state. Such table
is called a flip flop
excitation table.

9. Sequential Circuits
• A sequential circuit
is an interconnection
of flip-flops and
gates.
Example of a Sequential Circuit
Ax
Bx
Ax+Bx
A’x
x’
A+B (A+B).x
A=Ax+Bx, B=A’x
y=(A+B).x
State Table

10. Sequential Circuits
• A sequential circuit
is an interconnection
of flip-flops and
gates.
Example of a Sequential Circuit
Ax
Bx
Ax+Bx
A’x
x’
A+B (A+B).x
A=Ax+Bx, B=A’x
y=(A+B).x
State Table