Logic Gates

1. Digital Logic Design
IT101LGD
Prepared By
Asst. Lect. Mohammed Salim
Department of IT
1 LFU 2014

2. Grading
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 Course Grading:
Midterm Exam 25%
Course Work and Assignments 15%
Final Exam 60%
Total 100%

3. What does this chapter give you?
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 Identify the basic gates and describe the behavior of
each.
 Describe the behavior of a gate or circuit using
Boolean expressions, truth tables, and logic
diagrams.
 Combine basic gates into circuits.
 How to build half adder
and a full adder.

4. Contents
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Introduction
Logic Gates
Half-Adder
Full-Adder

5. Introduction
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Boolean functions may be practically implemented by
using electronic gates. The following points are
important to understand:
1- Electronic gates require a power supply.
2- Gate INPUTS are driven by voltages having two
nominal values, e.g. 0V and 5V representing logic 0
and logic 1 respectively.

6. Introduction
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3- The OUTPUT of a gate provides two nominal values
of voltage only, e.g. 0V and 5V representing logic 0
and logic 1 respectively. In general, there is only one
output to a logic gate except in some special cases.
4- There is always a time delay between an input
being applied and the output responding.

7. Introduction
Transistor Building Block of Computers
 Microprocessors contain millions of transistors
 Intel Pentium 4 (2000): 48 million
 IBM PowerPC 750FX (2002): 38 million
 IBM/Apple PowerPC G5 (2003): 58 million
 Logically, each transistor acts as a switch
Combined to implement logic functions
 AND, OR, NOT
 Combined to build higher-level structures
 Adder, multiplexer, decoder, register, …

8. Logic Gates – Binary Logic
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 Binary variables take one of two values.
 Logical operators operate on binary values and
binary variables.
 Basic logical operators are the logic functions AND,
OR and NOT.
 Logic gates implement logic functions.
 Boolean Algebra: a useful mathematical system for
specifying and transforming logic functions.
 We study Boolean algebra as a foundation for
designing and analyzing digital systems!

9. Logic Gates – Binary Variables
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 Remember that the two binary values have different
names:
 True/False
 On/Off
 Yes/No
 1/0
 We use 1 and 0 to denote the two values.
 Variable identifier examples:
 A, B, y, z

10. Logic Gates – Logical operations
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 The three basic logical operations are:
 AND
 OR
 NOT
 AND is denoted by a dot (·).
 OR is denoted by a plus (+).
 NOT is denoted by an overbar ( ¯ ), a single quote
mark (') after, or (~) before the variable.

11. Logic Gates – Notation Examples
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 Examples:
 is read “Y is equal to A AND B.”
 is read “z is equal to x OR y.”
 is read “X is equal to NOT A.”
Note: The statement:
 1 + 1 = 2 (read “one plus one equals two”)
is not the same as
 1 + 1 = 1 (read “1 or 1 equals 1”).
= BAY 
yxz +=
AX =

12. Logic Gates
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 A Logical gate is a device that performs a basic
operation on electrical signals, and these gates are
combined into circuits to perform more complicated
tasks.
 All basic logic gates have the ability to accept either
one or two input signals (depending upon the type of
gate) and generate one output signal.

13. Logic Gates Representation
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 There are three different methods for describing the
behavior of gates and circuits:
 Boolean expressions
 Logic diagrams
 Truth tables

14. Logic Gates Representation
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 Boolean expressions: expressions in this algebraic
notation are an smart way to show the activity of
electrical circuits.
 Logic diagrams: a graphical representation of a
circuit and each type of gate is represented by a
specific graphical symbol
 Truth tables: defines the function of a gate by listing
all possible input combinations that the gate could
encounter, and the corresponding output

15. Logic Gates
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 Let’s take the processing of the following six types of
gates:
 NOT
 AND
 OR
 NAND
 NOR
 XOR

16. NOT Gate
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 A NOT gate accepts only one input value
and produces one output value
 By definition, if the input value for a NOT gate is 0,
the output value is 1, and if the input value is 1, the
output is 0
 A NOT gate is sometimes called as an inverter
because it inverts the input value

17. AND Gate
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 An AND gate accepts two input signals.
 If the two input values for an AND gate are both 1,
the output is 1; otherwise, the output is 0

18. OR Gate
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 An OR gate accepts two input signals.
 If the two input values are both 0, the output value is
0; otherwise, the output is 1

19. XOR , or exclusive OR Gate
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 An XOR gate produces 0 if its two inputs are the
same, and a 1 otherwise.
 Note the difference between the XOR gate
and the OR gate; they differ only in one
input situation, when both input signals are 1, the OR
gate produces a 1 and the XOR produces a 0

20. NAND and NOR Gates
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 The NAND and NOR gates are basically the
opposite of the AND and OR gates, respectively:
 NAND gate:
 NOR gate:

21. Review of Logic Gates
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 A NOT gate inverts its single input value .
 An AND gate produces 1 if both input values are 1 .
 An OR gate produces 1 if one or the other or both input
values are 1 .
 An XOR gate produces 1 if one or the other (but not both)
input values are 1 .
 A NAND gate produces the opposite results of an AND
gate .
 A NOR gate produces the opposite results of an OR gate
.

22. Logic Gates Processor Example
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23. Half Adder
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 Half adder is a combinational logic circuit with two
input and two output. The half adder circuit is
designed to add two single bit binary number A and
B. It is the basic building block for addition of two
single bit numbers. This circuit has two
outputs carry and sum.

24. Half Adder
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25. Full Adder
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 Full adder is developed to overcome the drawback of
Half Adder circuit. It can add two one-bit numbers A
and B, and carry c. The full adder is a three input
and two output combinational circuit.

26. Full Adder
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27. Full Adder
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28. End of Chapter 3
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 Note : The PowerPoint slides are taken from internet websites and a
variety of presentations.
All the basic logic gates