Computer System Architecture lecture 12 GLAU

Binary Logic
• Definition of Binary Logic
– Binary logic consists of binary variables and a set of
logical operations.
– The variables are designated by letters of the
alphabet, such as A, B, C, x, y, z, etc, with each
variable having two and only two distinct possible
values: 1 and 0,
3

Logic gates
• Logic gates are the basic building blocks of any digital
system.
• It is an electronic circuit having one or more than one
input and only one output.
• The relationship between the input and the output is
based on a certain logic.
• Three basic logical operations:
• AND
• OR
• NOT.

AND Gate
• Truth Tables, Boolean Expressions are
x
y z
X y z
0 0 0
0 1 0
1 0 0
1 1 1
z = x • y = x y
The AND gate is an electronic circuit that gives a high output
(1) only if all its inputs are high. A dot (.) is used to show the
AND operation i.e. A.B. Bear in mind that this dot is
sometimes omitted i.e. AB

OR Gate
• The OR gate is an electronic circuit that gives a high output
(1) if one or more of its inputs are high. A plus (+) is used to
show the OR operation.
x y z
0 0 0
0 1 1
1 0 1
1 1 1
x
y z
z = x + y

• The NOT gate is an electronic circuit that produces an inverted
version of the input at its output. It is also known as
an inverter. If the input variable is x, the inverted output is
known as NOT x. This is also shown as x', or x with a bar
over the top.
x z
0 1
1 0
x z z = x’
NOT Gate

NAND Gate
Truth Table of NAND Gate
A NAND gate (NOT-AND) is a logic gate which produces an
output which is false only if all its inputs are true; thus its
output is complement to that of an AND gate. A LOW (0)
output results only if all the inputs to the gate are HIGH (1); if
any input is LOW (0), a HIGH (1) output results.

NOR Gate
Truth Table of NOR Gate
The NOR gate is a digital logic gate that implements
logical NOR -
A HIGH output (1) results if both the inputs to the gate are LOW
(0); if one or both input is HIGH (1), a LOW output (0) results.
NOR is the result of the negation of the OR operator.

Universal Gate
• NAND and NOR Gates are called Universal Gates because AND,
OR and NOT gates can be implemented &created by using these
gates.
NAND Gate Implementations NOR Gate Implementations

Special Purpose Gate
• EX-OR Gate
• EX-NOR Gate

EX-OR Gate
Truth Table of EX- OR Gate
Exclusive OR gate –
is a digital logic gate that gives a true (i.e. a HIGH or 1) output when
the number of true inputs is odd. ...
An XOR gate is normally two inputs logic gate where the output is
only logical 1 when only one input is logical 1
(A’.B) + (A.B’) or A B
⊕

EX-NOR Gate
Truth Table of EX-NOR Gate
An XNOR gate (sometimes referred to by its extended
name, Exclusive NOR gate)
It is a digital logic gate with two or more inputs and one output
that performs logical equality.
The output of an XNOR gate is true when all of its inputs are
true or when all of its inputs are false.
(A.B) + (A.B)’ or ( A B)’
⊕

Computer System Architecture lecture 12 GLAU

Computer System Architecture lecture 12 GLAU

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Computer System Architecture lecture 12 GLAU