1.
Submitted by:
Warda Aziz (101631058)
Submitted to:
Miss Amna Dilawar
Date of submission
Subject title:
Digital logic and comupter designing
Govt. PostGraduate ColleGe for Women
samnabd, lahore

2.
Table of contents:
➣ Combinational logic circuit
➣ Programmable logic devices
➣ PLA over read-only memory
➣ Programmable logic array (PLA)
Block diagram of PLA
Internal construction of a specific PLA
Implementation procedure
Related problem
➣ Question 2:-
Difference between combinational and logical circuit
Combinational logic circuits
Sequential logic circuits.
➣ Reference:

3.
➣ Combinational logic circuit:
Combinational circuit is a circuit in which we combine the different gates in the
circuit, for example encoder, decoder, multiplexer and de-multiplexer. The output of
combinational circuit at any instant of time, depends only on the levels present at input
terminals. The combinational circuit do not use any memory.
Or
In digital circuit theory, combinational logic (sometimes also referred to as time-independent
logic) is a type of digital logic which is implemented by Boolean circuits, where the output is
a pure function of the present input only. This is in contrast to sequential logic, in which the
output depends not only on the present input but also on the history of the input
➣ Programmable logic devices:
A programmable logic device (PLD) is an electronic component used to build
reconfigurable digital circuits. Unlike a logic gate, which has a fixed function, a PLD
has an undefined function at the time of manufacture. Before the PLD can be used in
a circuit it must be programmed, that is, reconfigured.
➣ PLA over read-only memory
A combinational circuit may occasionally have don’t care conditions. When implemented
with ROM a don’t care conditions becomes an address input that will never occur. The words
at the don’t care addresses need not to be programmed and may be left in their original state
(all 0’s or all 1’s).
For cases where the number of don’t care conditions is excessive it is more
economical to use a second type of LSI component called programmable logic array. A PLA
is similar to ROM in concept; however, The PLA does not provide full decoding of the
variables and does not generate all the minterms as provided in RAM.
➣ Programmable logic array (PLA)
A programmable logic array (PLA) is a kind of programmable logic device used to
implement combinational logic circuits. The PLA has a set of programmable AND gate
planes, which link to a set of programmable OR gate planes, which can then be conditionally
complemented to produce an output.
The no. of programmable links in PLA is 2n *k + k*m + m, whereas that of rom is
2n
*m.
BLOCK DIAGRAM OF PLA:
Internal construction of a specific PLA:
STEP 1:
K product
terms (AND
gates)
M sum
terms (OR
gates)

4.
STEP 2:
The next part is to draw a vertical wire with an AND gate
STEP 3:
The first AND gate (on the left) is the min term: x2’.x1’.x0
The second AND gate (from the left) is the minterm: x2’.x1.x0
The third AND gate (from the left) is the minterm: x2’.x1’.x0’
I’ve added a fourth AND gate which is the minterm: x2.x1.x0.
STEP 4:
We then add OR gates using horizontal wires, to connect the minterms together.
Implementation procedure
1. Preparation in SOP (sum of products) form.
2. Obtain the minimum SOP form to reduce the number of product terms to a minimum.
3. Decide the input connection of the AND matrix for generating the required product
term.

5.
4. Then decide the input connections of OR matrix to generate the sum terms.
5. Decide the connections of invert matrix.
6. Program the PLA.
Let’s try to implement these function f1 and f2 are given as
Inputs x1, x2, x3 and their respective complemented signals are given to programmable AND
plane, there we will get AND plane outputs as P1, P2, P3called minterms. Then these signals
are given to programmable OR plane to produce required output function f1 and f2 (sum of
products). The below figure describes the gate level implementation of the PLA for given
functionality.

6.
Related problem:
Derive the PLA program table for a combinational circuit that squares s 3-bit
number.
Solution:
PLA program table:
A B C F1 F2 F3 F4
0 0 0 0 0 0 0
0 0 1 0 0 0 0
0 1 0 0 0 0 1
0 1 1 0 0 1 0
1 0 0 0 1 0 0
1 0 1 0 1 1 0
1 1 0 1 0 0 1
1 1 1 1 1 0 0
K-map for F1:
B’C’ B’C BC BC’
A 1 1
A’
K-map for F1’:
B’C’ B’C BC BC’
A 0 0
A’ 0 0 0 0
F1= AB F1’=A’+B’
K-map for F2:
B’C’ B’C BC BC’
A 1 1 1
A’
K-map for F2’:
B’C’ B’C BC BC’
A 0
A’ 0 0 0 0
F2= AB’+AC F2’=A’+BC’
K-map for F3:
B’C’ B’C BC BC’
A 1
A’ 1

7.
K-map for F3’:
B’C’ B’C BC BC’
A 0 0 0
A’ 0 0 0
F3= AB’C+A’BC F3’=A’B’+AB+C’
K-map for F4:
B’C’ B’C BC BC’
A 1
A’ 1
K-map for F4:
B’C’ B’C BC BC’
A 0 0 0 1
A’ 0 0 0 1
F4= BC’ F4’=B’+C
PROGRAM TABLE:
A B C F1 F2 F3 F4
AB 1 1 - 1 - - -
A’ 0 - - - 1 - -
BC’ - 1 0 - 1 - 1
A’B’ 0 0 - - - 1 -
C’ - - 0 - - 1 -
T C C T
Question 2:-
Difference between combinational and logical circuit
Combinational logic circuits.
The simple time independent logic circuits that are implemented using Boolean circuits
whose output logic value depends only on the input logic values can be called as
combinational logic circuits.

8.
Sequential logic circuits.
The simple logic circuits whose output logic value depends on the input logic values and also
on the stored information is called as sequential logic circuits.
Major differences:
Combinational logic circuits Sequential logic circuits
These combinational digital logic circuits
don’t have the capability to store a state
inside them.
These sequential digital logic circuits are
capable to retain the earlier state of the
system based on the current inputs and
earlier state.
the combinational logic circuits do not
contain any memory elements
The sequential logic circuits contain
memory elements.
The combinational digital logic circuits are
fundamentally implemented using different
types of devices such as multiplexers, de-
multiplexers, encoders, decoders, half
adder, and full adders.
The latch is considered as the simplest
element used to retain the earlier memory or
state in the sequential digital logic.
As there are no clocks used in these digital
logic circuits, they do not need any
triggering
The maximum number of sequential logic
circuits uses a clock for triggering the flip
flops operation
The combinational digital circuits don’t
require any feedbacks
The sequential digital logic circuits utilize
the feedbacks from outputs to inputs.

9.
Reference:
www.elprocus.com/sequential-circuit-design-using-pla/
http://www.edgefx.in/wp-content/uploads/2015/02/Combinational-Logic-Circuit.jpg
Digital logic & computer design by Morris Mano