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Logic Gate And Logic Circuit and Motherboard (Logic Gates (Gate is an…
Logic Gate And Logic Circuit and Motherboard
INTRO
• Boolean algebra is the branch of algebra in
which the values of the variables are the truth
values true and false, usually denoted 1 and 0
respectively.
• derives its name from the mathematician
George Boole.
Boolean expression is an expression that
results in a boolean value, that is either true
or false
– Variables are represented by letters and can have
one of two values, either 1 or 0.
– Boolean operations are carried out with logical
operators.
– Logical operators in Boolean algebra are AND (.),
OR (+), and NOT (’).
LOGICAL OPERATOR
AND
Logical AND of A and B is written as A . B and
read as “A and B”.
• It is True if and only if both of A and B are
True.
• The Boolean equation for AND operation can
be written as Y = A • B, or Y = AB, or Y = A∩B.
• The ∩ symbol is pronounced "intersection”.
OR
Logical OR of A and B is written as A + B and
read as “A or B”.
• It is True if either A or B, or both are True.
• The Boolean equation for OR operation can be
written as Y = A + B or Y = A ∪ B.
• The ∪ symbol is pronounced “union”
NOT
• The complement (or negation) of A is written
as A’ or and read as “not A”.
• If A is True then A’ or is False.
• If A is False then A’ or is True.
• The Boolean equation for NOT operation is
written as Y = A’
Logic Gates
Gate is an electronic circuit in which the input
and output represent the statement of
Boolean algebra.
Truth Table
• A truth table is used to show the function of a
logic gate.
• It shows the output states for every possible
combination of input states.
• For a logic gate with n input, there are 2
n rows
in the truth table.
• Each row will represent different combination
of input states
AND
• The AND gate has two binary input and one
binary output.
• The AND gate produces a TRUE output if and
only if both A and B are TRUE.
• The Boolean expression for AND gate can be
written in three ways:
Y = A • B, Y = AB, or Y = A ∩ B.
Logic Gate: OR
• The OR gate has two binary input and one
binary output.
• The OR gate produces a TRUE output if either
A or B (or both) is TRUE.
• The Boolean equation for an OR gate is
written as Y = A + B or Y = A ∪ B.
NOT
• The NOT gate has one binary input and one
binary output.
• The output of NOT gate is the inverse of its
input. TRUE input will produce FALSE, and
FALSE input will produce TRUE.
• The Boolean equation for NOT gate is written
as Y = A’
NAND
• Combination of AND and NOT gate.
• NAND gate produce TRUE output when any of
the input is FALSE.
• Produce FALSE output when all of the input
are TRUE.
• The Boolean expression for NAND gate can be
written in three ways:
Y = A • B, Y = AB, or Y = A ∩ B.
NOR
• Combination of OR and NOT gate.
• Produce TRUE output when all of the input
are FALSE.
• Produce FALSE output when any of the input
is TRUE.
• The Boolean equation for an NOR gate is
written as Y = A + B or Y = A ∪ B.
Motherboard
Components of a Motherboard
• Processor Slot
• Memory Slot
• Adapter Card Slot
• SATA connector
• BIOS chip and battery
• Power connector
Processor Slot
• A slot on the motherboard that holds a
processor chip.
Memory Slot
• Slots on the motherboard that hold memory
modules.
• Memory module is a small circuit board that
holds RAM chips.
Adapter Card Slot
• Slots on the motherboard that hold adapter
cards.
• Adapter card slots are also called expansion
slots.
AGP slot
– Specifically designed to connect graphic adapters.
PCI slot
– To connect devices such as network cards, sound
cards, modems, extra ports such as USB or serial
TV tuner cards and disk controllers.
Machine Cycle
Steps in a Machine Cycle 1) Fetch - Control unit fetches the instruction
and data from memory.
2) Decode - Control unit interprets the
instruction and sends the instruction and
data to the ALU.
3) Execute - ALU performs calculations on the
data.
4) Store - The results of the calculations are
stored in the memory