LOGIC CIRCUITS AND DESIGN

Module 1- Logic Gates

By: Engr. Irene F. Salvador, MSME

Logic Circuits and Devices
Module 1: Logic Gates

TOPIC PRE
OUTLINE ASSESSMENT

A. Basic Logic Gates Answer the following questions.

B. Universal Logic Gates
1. What is the largest binary number that can be
C. Exclusive Logic Gates expressed with 16 bits?

2. What are the equivalent decimal and hexadecimal

LEARNING numbers of your answer in no. 1?
OBJECTIVES ,

At the end of this module, you should be able to: 3. Obtain the 1’s and 2’s complements of the
following binary numbers:
1. Learn the different types of logic gates. (a) 00010000
2. Understand the functions of each Logic gates in dig- (b) 00000000
ital design. (c) 11011010
3. Derive the equation from a circuit diagram.
4. Use the logic gate in a working mechanism/circuit, LOGIC
GATES

OVERVIEW A logic gate is a building block of a digital circuit. Most

logic gates have two inputs and one output and are
based on Boolean algebra. At any given moment, every
Computers have become as the basic need in our terminal is in one of the two binary conditions false
day-to-day life. Computers are basically used to (high) or true (low). False represents 0, and true
perform multitude of tasks, operations, and represents 1. Depending on the type of logic gate being
computations within quite less amount of time. One of used and the combination of inputs, the binary output
the significant functions of the CPU in a computer is to will differ.[2]
perform a logical operation which is done by utilizing
A logic gate can be thought of like a light switch,
some hardware, including electronic kits, chips and
wherein one position the output is off—0, and in
integrated circuits and software (programming)
another, it is on—1. Logic gates are commonly used in
technologies. But, how these hardware and software
integrated circuits (IC). Digital systems are said to be
interact and perform all these operations is quite a big
constructed by using logic gates. These gates are the
puzzle.
AND, OR, NOT, NAND, NOR, EXOR and EXNOR gates.
In order to have a better understanding of such a The basic operations are described below with the aid
complex issue, we must have to acquaint with the term of truth tables.
Boolean Logic, developed by George Boole. We are
aware of the fact that computers utilize binary digits
instead of decimal digits for ease of operation. All the
logical operations are carried out by the logic gates.[1]

Figure 1: Block Diagram

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Logic Circuits and Devices
Module 1: Logic Gates

inverted output is known as NOT A as shown in Figure

BASIC LOGIC 4. This is also shown as A’, or A with a bar over the top,
GATES as shown at the outputs.

AND GATE
IMPLEMENTATION OF
BASIC LOGIC GATES

The implementation of the basic logic gate is to make a

simple circuit interconnecting the And, Or and NOT gate
with the input variables A,B and C. The output equation
was formulated from the flow of the circuit as shown in
figure 5.0. As the input variables A and B goes into the
Figure 2: AND Gate And gate, the operation of multiplying A and B will be
performed, then the output of And gate will now be A.B
or just AB. Then on the next logic gate which is the OR
The AND gate is an electronic circuit that gives a high gate, the inputs will be the output of of the And gate
output (1) only if all its inputs are high (1),otherwise the (AB) and the other variable which is C will pass through
output is low (0) as you could see in the function table. not gate so it will be inverted as C’. These two inputs
A dot (.) is used to show the AND operation (i.e. A.B). will go through the OR gate and the operation of
Bear in mind that this dot is sometimes omitted i.e. AB addition will be performed having now the output of
as shown in Figure 2. (AB + C 0 ). The output of the Or gate will now be an
input to the next AND gate in the circuit together with
the variable C, but this time, the variable C did not pass
OR GATE through Not gate. So these inputs(AB + C 0 ) and C will
be multiplied as it goes through the last And gate, then
the final output og the circuit will be (AB + C 0 )C.

Figure 3: OR Gate

The OR gate in figure 3.0 is an electronic circuit that

gives a high output (1) if one or more of its inputs are Figure 5: Basic Logic Gate Circuit
high. A plus (+) is used to show the OR operation.

UNIVERSAL
NOT GATE LOGIC GATES

The NAND and NOR gates are the universal gates. Each
of this gates can realize the logic circuits single
handedly. The NAND and NOR are also called as
universal building blocks. Both NAND and NOR has the
ability to perform three basic logic functions such as
Figure 4: NOT Gate AND,OR and NOT. NAND gate is a combination of an
AND gate and a NOT gate. The expression for the
NAND gate is ‘—‘whole bar. The output of the NAND
The NOT gate is an electronic circuit that produces an gate is at logic 0 level only when each of the inputs
inverted version of the input at its output. It is also assumes a logic 1 level. The truth table of two-input
known as an inverter. If the input variable is A, the NAND gate is given below:

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Logic Circuits and Devices
Module 1: Logic Gates

NAND GATE input for Nor gate, together with the input C. These
inputs now will go through the Nor gate, it will be added
first and then inverted, so the output equation of the
circuit will be ((AB)0 + C)0 .

Figure 6: NAND Gate

Figure 8: NAND and NOR Circuit

The NAND gate in figure 6 is the same as AND gate
with NOT gate connected at the output. The circle at
the output of the NAND gate is called bubble, an EXCLUSIVE
inverter absorbed by the And gate. The equation at the LOGIC GATES
output (AB)0 means that the inputs A and B are
multipled first, that is why it is enclosed with a
XOR GATE (Exclusive OR)
parenthesis and the product then will now be inverted
as signified by the (prime- ’) after the (AB).

NAND GATE

Figure 9: XOR Gate

The function of exclusive OR gate, as shown in figure 9

that if the inputs are not the same or the other input is
high (1) and the other input is low (0), the output is high
Figure 7: NOR Gate (1), otherwise the output is low (0). It uses an operator
symbol ⊕, so the output equation will be A ⊕ B.The
other way to express the equation for XOR gate is
The NOR gate in figure 7 is also the same as OR gate (A0 B + AB 0 ).
with NOT gate connected at the output. The inputs A
and B will be added first before it will be inverted as
shown in the output equation (A + B)0 . On the function XNOR GATE (Exclusive NOR)
table, if the inputs A and B are both low (0), so when
(A = 0) + (B = 0), the sum will be 0 and will be inverted
to 1. If one of the input is high (1) the sum will be 1 and
will be inverted to 0.

IMPLEMENTATION OF
UNIVERSAL LOGIC GATES
Figure 10: XNOR Gate
The illustration of the interconnected NAND and NOR
gate in figure 8 shows that the inputs A and B will pass The symbol for XNOR gate, as illustrated in figure ?? is
through NAND gate and will have an output of A just like XOR gate but with a bubble on the output which
multiplied to B, then inverted using a (’). The output means that, outputs are inverted. The function of XNOR
equation,(AB)0 of NAND gate will now be one of the is totally the reverse of XOR wherein the output will be

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Module 1: Logic Gates

high (1), if both inputs A and B are the same high (1) or 2. The Inverter is also called
the same low (0). The output equation for XNOR can be
given in many forms other than the output equation in a) Not Gate b) And Gate
figure ?? c) Or GAte d) Xor Gate
¯ B)
(A ⊕ (1)
3. The NOR gate is OR gate followed by
or
..................
(A ⊕ B)0 (2)
or a) And Gate b) Nand Gate
0 0
(AB + A B ) (3) c) Not GAte d) None of the above

4. The only function of NOT gate is to . . . . . . . . . . . . . . . ..

IMPLEMENTATION OF a) Stop signal b) Invert input signal
EXCLUSIVE GATES c) Act as universal d) Amplify the signal
gate on the output
The circuit in figure 11, shows two xor gates connected
as inputs for the Xnor. The inputs for the first Xor gate 5. When an input signal 1 is applied to a NOT gate, the
are A and B with an output equation of (A ⊕ B) while output is . . . . . . . . . . . . . . . . . .
the second Xor gate has B and C as its inputs with an a) 0 b) 1
output equation of (B ⊕ C) . The output equation of
both Xor will now be the input for the Xnor, so the final c) Either 0 and 1 d) nothing happens to
output equation of the circuit is the signal

6. The output will be a LOW for any case when one or

¯ (B ⊕ C)
(A ⊕ B) ⊕ (4) more inputs are zero in a/an . . . . . . . . . . . .

a) Or gate b) Not Gate

or it could be presented as the equation in the figure
below. The small bar over the operator of Eqn.(4) is the c) And Gate d) Nand Gate
same as the long bar over the equation in figure 11.
7. The logic gate that will have HIGH or “1” at its
output when any one of its inputs is HIGH is a/an
. . . . . . . . . . . . . . . gate.

a) Or Gate b) Not Gate

c) And Gate d) Nand Gate

8. A NAND gate has . . . . . . .. inputs and . . . . . . . output.

a) LOW inputs and b) HIGH inputs and

LOW outputs HIGH outputs
Figure 11: XNOR and XOR Circuit c) LOW inputs and d) None of these
HIGH outputs

9. The basic logic gate whose output is the

complement of the input is . . . . . . . . . . . . .
ACTIVITY
a) Or Gate b) And Gate

A. Multiple Choice Questions: Choose the correct c) Not Gate d) Nor Gate
answer.
10. . . . . . . . . . . .. input values will cause an AND logic
gate to produce a HIGH output.
1. The universal gate is . . . . . . . . . . . . . . . . . .
a) At least one input is b) At least one input is
a) Nand Gate b) Or Gate HIGH LOW

c) And Gate d) None of the Above c) All inputs are HIGH d) All inputs are LOW

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Logic Circuits and Devices
Module 1: Logic Gates

11. The logic gate that will have HIGH or “1” at its
output when any one of its inputs is HIGH is a(n):

a) Or Gate b) And Gate

c) Nor Gate d) Not Gate

12. What input values will cause an AND logic gate to

produce a HIGH output? C.

a) All inputs are LOW. b) At least one input is

HIGH.

c) At least one input is d) All inputs are HIGH.

LOW.

13. The output will be a LOW for any case when one or
more inputs are zero in a(n):
SUMMARY
a) Or Gate b) Not Gate

c) And Gate d) Nand Gate The Logic gates consists the basic gates, the universal
gates, and the exclusive gates.. The basic logic gates
14. The boolean expression of an OR gate is are And, Or and N ot. The And Gate will only have a
high ouput (1), only if both inputs are high (1), otherwise
a) A.B b) A0 B + AB 0
the output is low (0). The Or Gate will only have a low
c) A + B d) A0 B 0 output (0), only if both inputs are low (0), otherwise the
output is high (1). The N ot Gate, also called the
15. The expression of an XOR gate is inverter will give a high (1) output if the input is low (0)
but if the input is high (1), the output will be low (0).
a) A0 B + AB 0 b) AB + A0 B 0
The Universal gates are N and and N or, where the
c) A + A.B d) A0 + B 0 N and is an And gate with N ot gate on the output, that is
why there is a bubble on the output of the N and Gate.
The N or Gate is also an Or gate with a N ot Gate on the
B. Write the output expression of the following circuit output. Both these gates functioned as the reverse of
diagrams. the And gate for N and and Or gate for N or.

The Exclusive gates are XOr and XN or gates where

XOr is also called exclusive-OR and XN or is an
exclusive-NOR. These two exclusive gates functions as
the reverse of each other. The XOr will just have a high
output (1), if both inputs are unequal, but if the inputs
are equal, the output will be low (0). The XN or will only
have a high output (1), if both inputs are equal, but if
inputs are unequal, then output will be low (0).
A. The implementation of these gates will only be tested
or simulated when applying an input signal and an
output component to identify if it is high or low. The
ouput equation or expression will be determined from
the circuit flow. If inputs passes through AN D gate, the
operator used will be a dot (.) for multiplication, when
passed through OR gate, the operator used will be plus
(+), for addition and when an input goes through N OT
gate, the input will be inverted having a bar (-) over the
variable or expression or a prime (’) signifying that the
B. input was inverted.

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Logic Circuits and Devices
Module 1: Logic Gates

REFERENCES

[1] Mano, Morris and Michael D. Ciletti Digital De-

sign, 5th edition. Pearson Education, Inc. New Jersey,
USA.(2013)
[2] https://www.circuitstoday.com/logic-gates

[3] https://www.tutorialspoint.com/computer-logical-
organization/logic-gates.htm
[4] https://www.elprocus.com/basic-logic-gates-with-
truth-tables

Prepared by:
ENGR. IRENE F. SALVADOR, CPE, MSME
Faculty, Computer Engineering Department
College of Engineering and Architecture

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