Arithmetic and logic unit

Unit 2
Arithmetic and Logic Unit (ALU)

Bus:
In computer architecture, a bus is a communication system that transfers data between components inside a computer,
or between computers. This expression covers all related hardware components (wire, optical fiber, etc.) and software,
including communication protocols.
Early computer buses were parallel electrical wires with multiple hardware connections, but the term is now
used for any physical arrangement that provides the same logical function as a parallel electrical bus. Modern computer
buses can use both parallel and bit serial connections, and can be wired in either a multi drop (electrical parallel) or
daisy chain topology, or connected by switched hubs, as in the case of USB.
2/3/2019BY M INDRAJA 2

ALU stands for Arithmetic Logic Unit:
It is a digital circuit that performs Arithmetic (Add,Sub,…) and Logical
(AND,OR,NOT) operations
This architecture was proposed by John Von Neumann in 1945 when he was
working on EDVAC (Electronic discrete variable automatic computer)

Introduction:
Logic gate are the basic building blocks of any digital system. It is an electronic circuit having 1 or more
than 1 input and only one output. The relationship between the input and output is based on a certain logic.
Based on this, logic gates are named as and gate, or gate, NOT gate et…
Logic gates are mostly implemented using electronic switches like diodes or
transistors, but can also be built using electromagnetic relays, vacuum tubes, fluidic logic, optics, etc.
In computers or control units, a large number of electronic circuits are made up of logic gates. These
processes signals are denoted by T (True) or F (False).
Logic gates are mainly used in some devices like microprocessors, embedded systems,
microcontrollers, registers, ALUs, MUX and also in computer memory; there are more than 100 million
gates especially in microprocessors.

Definition of Logic Gate:
A logic gate is a basic building block of a circuit used to make a large number of electronic
circuits.
Types of Logic Gates:
Different types of logic gates include AND,OR,NOT,NAND,NOR,EX-OR,EX-NOR

AND Gate :
When both the inputs are high, then the output is high, otherwise
the output is low.

OR Gate:
If any of the input is high, then the output is high

NOT Gate:
The output is inversely proportional to the input.

NAND Gate :
If both the inputs are high, then the output is low, otherwise high

NOR Gate: If both the inputs are low, then the output is high otherwise low.

EX-OR Gate:
If both the inputs are high or low, then the output is low, otherwise high.

EX-NOR Gate:
If both the inputs are high or low, then the output is high, otherwise low.

Arithmetic Circuit:
Binary Adder : Binary adder is used to add two binary numbers.
In general, the adder circuit needs two binary inputs and two binary outputs. The input
variables designate the x and y; Then the output variables produce the sum and carry.
The binary addition operation of single bit is shown in the truth table
In fourth case, a binary addition is creating a sum of (1 + 1 = 10) i.e. 0 is written in the given
column and a carry of 1 over to the next column.

The simplified sum of products expressions are
The circuit implementation is
This circuit can not handle the carry input, so it is termed as half adder.

Half Adder:
A half adder is a type of adder, an electronic circuit that performs the addition of
numbers. The half adder is able to add two single binary digits and provide the
output plus a carry value.
It has 2 inputs, called A and B, twso outputs S (sum) and C (carry).
The common representation uses a XOR logic gate an AND logic gate.
Full Adder:
A full adder is a combinational circuit that forms the arithmetic sum of three inputs
and two outputs.
Two of the input variables, denoted by x and y, represented the two bits to be
added.The third input Z, represents the carry from the previous lower position.
The two outputs are designated by the symbols S for sum and C for carry

Ripple Carry Adder:
 The ripple carry adder is constructed by cascading full adder blocks in series.
 The carryout of one stage is fed directly to the carry-in of the next stage
 For an n-bit ripple adder , it requires n full adders.

Carry Look Ahead Adder:
A carry-lookahead adder (CLA) or fast adder is a type of adder used in digital logic.
A carry-lookahead adder improves speed by reducing the amount of time required to determine
carry bits. It can be contrasted with the simpler, but usually slower, ripple-carry adder (RCA), for
which the carry bit is calculated alongside the sum bit, and each stage must wait until the previous
carry bit has been calculated to begin calculating its own sum bit and carry bit. The carry-
lookahead adder calculates one or more carry bits before the sum, which reduces the wait time to
calculate the result of the larger-value bits of the adder.

Booth’s Algorithm:
Booth algorithm gives a procedure for multiplying binary integers in signed 2’s complement
representation in efficient way, i.e., less number of additions/subtractions required. It operates on the fact
that strings of 0’s in the multiplier require no addition but just shifting and a string of 1’s in the multiplier
from bit weight 2^k to weight 2^m can be treated as 2^(k+1 ) to 2^m.
As in all multiplication schemes, booth algorithm requires examination of the multiplier bits and shifting
of the partial product. Prior to the shifting, the multiplicand may be added to the partial product, subtracted
from the partial product, or left unchanged according to following rules:
1. The multiplicand is subtracted from the partial product upon encountering the first least significant 1 in
a string of 1’s in the multiplier
2. The multiplier is added to the partial product upon encountering the first 0 (provided that there was a
previous ‘1’) in a string of 0’s in the multiplier.
3. The partial product does not change when the multiplier bit is identical to the previous multiplier bit.

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ALL THE BEST

Arithmetic and logic unit

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