COLLEGE OF ENGINEERING
CENTRAL PHILIPPINE UNIVERSITY
ILOILO CITY, PHILIPPINES
Tel Nos. (033) 329 1971 (to 79) local 1084
EE/ECE DEPARTMENT
LABORATORY EXPERIMENT NO. 4
SYNTHESIZING
COMBINATIONAL
LOGIC CIRCUITS
ECE 4104
Logic and Switching Theory
(10 1130 TH)
Submitted by:
Deatras, Job D.
Yap, Alvin Jan E.
Submitted to:
Engr. Ramon Alguidano, Jr.
I. OBJECTIVES
1. To identify the minterms (product terms) and maxterms (sum terms).
2. To analyze the behavior of a logic circuit by constructing a truth
table that lists the relationship between input variable combinations
and output variable.
3. To realize a combinational function directly using basic gates (NOT,
AND, OR, NOR, and NAND).
II. BASIC THEORY
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. In other words,
sequential logic has memory while combinational logic does not.
Combinational logic is used in computer circuits to perform Boolean
algebra on input signals and on stored data. Practical computer circuits
normally contain a mixture of combinational and sequential logic. For
example, the part of an arithmetic logic unit, or ALU, that does mathematical
calculations is constructed using combinational logic. Other circuits used in
computers, such as half adders, full adders, half subtractors, full subtractors,
multiplexers, demultiplexers, encoders and decoders are also made by using
combinational logic.
III. SCHEMATIC DIAGRAM/TABLE
(USE GRAY CODE, SOP & BOOLEAN
ALGEBRA)
A
B
C
D
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
IV. EQUIPMENT/INSTRUMENTS/MATERIALS NEEDED
Computer Simulation (TINA)
Logic Gates
V. PROCEDURES AND RESULTS
1. Write the sum of products expression based on the truth table for the
logic function.
2. Implement this expression using standard logic gates. (We may not get
the most efficient implementation this way, but we can simplify the
circuit afterwards)
A
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
B
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
USING GRAY CODE
C
D
W
X
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
Y
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
Z
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
VI. OBSERVATION
Based from the results gathered the group has observed that
combinational logic gates are made up from basic logic NAND, NOR or NOT
gates that are combined or connected together to produce more
complicated switching circuits. In what has observed, in synthesizing these
combinational logic gates, the use of Boolean algebra is needed and also can
be verified using Karnaugh Map. It was also observed that getting the
minterms (sum-of-products) is used to get the equations and later on
simplified through Boolean algebra. The group have verified the table above
using Gray Code, as well as Boolean through manual computation and was
also verified through computer simulation with its logic design. The results
arrived to what is expected and was observed that the use of basic logic
gates is needed to create a circuit after arriving to the results of the
computation.
VII. CONCLUSION
Based from the results gathered the group has concluded that after
applying Gray code with the truth table, getting the minterms (sum-ofproducts) is needed to further simplify and construct a circuit using the
simplified equation. Minterm is the name given to the case where the given
possibility in a digital "word" is boolean one and all of the other cases are
boolean zero, using binary as a basis. The minterms are taken from the logic
one outputs in which all logic one inputs are not complemented while all
logic zero inputs are complemented.
Combinational logic circuits are consist of inputs, two or more basic
logic gates and outputs. The logic gates are combined in such a way that the
output depends entirely on the inputs. A combinational logic circuit performs
an operation assigned logically by a Boolean expression or Karnaugh Map
and even the truth table by using the minterms as well as using the Gray
code. Combinational logic circuits can be very simple or very complicated
and any combinational circuit can be implemented with only NAND and NOR
gates as these are classed as universal gates.
VIII. DESIGN APPLICATION
One of the most common uses of combinational logic is in multiplexer
and de-multiplexer type circuits. Here, multiple inputs are connected to a
common signal line and logic gates are used to decode an address to select
a single data input or output switch. Common combinational circuits made
up from individual logic gates that carries out a desired application include
multiplexers, de-multiplexers, encoders, decoders, full adders, half adders,
and etc.
As an example of using several circuits together, we are going to make a
device that will have 16 inputs, representing a four digit number, to a four
digit 7-segment display but using just one binary-to-7-segment encoder.
First, the overall architecture of our circuit provides what looks like the
description provided.
Follow this circuit through and you can confirm that it matches the
description given above. There are 16 primary inputs. There are two more
inputs used to select which digit will be displayed. There are 28 outputs to
control the four digit 7-segment display. Only four of the primary inputs are
encoded at a time. You may have noticed a potential question though.
When one of the
display? Review
any
line
not
and
digits are selected, what do the other three digits
the circuit for the demultiplexers and notice that
selected by the A input is zero. So the other
three digits are blank. We don't have a problem,
only one digit displays at a time.
Notice how quickly this large circuit was
developed from smaller parts. This is true of
most complex circuits: they are composed of
smaller parts allowing a designer to abstract
away some complexity and understand the
circuit as a whole. Sometimes a designer can
even take components that others have designed
remove the detail design work.
In addition
to the added quantity of gates, this design
suffers
from one additional weakness. You can only see
one
display one digit at a time. If there was some way to rotate
through the four digits quickly, you could have the appearance of all four
digits being displayed at the same time. That is a job for a sequential circuit.
IX. COMPUTER SIMULATION
OUTPUT (W)
OUTPUT (X)
OUTPUT (Y)
OUTPUT (Z)
