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Course Material (Lecture Notes)
CS6303 – COMPUTER ARCHITECTURE
LESSION NOTES
UNIT II
ARITHMETIC OPERATIONS
ALU
In computing an arithmetic logic unit (ALU) is a digital circuit that performs arithmetic
and logical operations. The ALU is a fundamental building block of the central processing unit
(CPU) of a computer, and even the simplest microprocessors contain one for purposes such as
maintaining timers. The processors found inside modern CPUs and graphics processing units
(GPUs) accommodate very powerful and very complex ALUs; a single component may contain
a number of ALUs.
Mathematician John von Neumann proposed the ALU concept in 1945, when he wrote a
report on the foundations for a new computer called the EDVAC. Research into ALUs
remains an important part of computer science, falling under Arithmetic and logic
structures in the ACM Computing Classification System
FIXED POINT NUMBER AND OPERATION
In computing, a fixed-point number representation is a real data type for a number that
has a fixed number of digits after (and sometimes also before) the radix point (e.g., after the
decimal point '.' in English decimal notation). Fixed-point number representation can be
compared to the more complicated (and more computationally demanding) floating point number
representation.
CS6303 – COMPUTER ARCHITECTURE
UNIT-II
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Course Material (Lecture Notes)
Fixed-point numbers are useful for representing fractional values, usually in base 2 or base
10, when the executing processor has no floating point unit (FPU) or if fixed-point provides
improved performance or accuracy for the application at hand. Most low-cost embedded
microprocessors and microcontrollers do not have an FPU.
FLOATING POINT NUMBERS & OPERATIONS
Floating point Representation:
To represent the fractional binary numbers, it is necessary to consider binary point.If
binary point is assumed to the right of the sign bit ,we can represent the fractional binary
numbers as given below,
Direct implementation of dedicated units :
always : 1 – 5
in most cases : 6
sometimes : 7, 8
Sequential implementation using simpler units and
several clock cycles (_decomposition) :
sometimes : 6
in most cases : 7, 8, 9
Table lookup
techniques using ROMs :
universal : simple application to all operations
efficient only for singleoperand operations of high
complexity (8 – 12) and small word length (note: ROM size
Approximation techniques using simpler units : 7–12
�taylor series expansion
�polynomial and rational approximations
�convergence of recursive equation systems
Binary adder
This is also called Ripple Carry Adder, because of the construction with full adders are
connected in cascade.
CS6303 – COMPUTER ARCHITECTURE
UNIT-II
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Course Material (Lecture Notes)
Carry Look Ahead Adder
The most widely used technique employs the principle of carry look-ahead to improve
the speed of the algorithm.
Binary subtractor
Usually there are more bits in the partial products and it is necessary to use full adders to
produce the sum of the partial products.
For J multiplier bits and K multiplicand bits we need (J X K) AND gates and (J − 1) Kbit adders to produce a product of J+K bits.
K=4 and J=3, we need 12 AND gates and two 4-bit adders.
ALU stands for: Arithmetic Logic Unit
ALU is a digital circuit that performs Arithmetic (Add, Sub, . . .) and Logical (AND, OR,
NOT) operations.
John Von Neumann proposed the ALU in 1945 when he was working on EDVAC
Typical Schematic Symbol of an ALU
1-Bit ALU
This is an one-bit ALU which can do Logical AND and Logical OR operation.
Result = a AND b when operation = 0
Result = a OR b when operation = 1
The operation line is the input of a MUX
CS6303 – COMPUTER ARCHITECTURE
UNIT-II
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Course Material (Lecture Notes)
32-Bit ALU
ADDITION AND SUBTRACTION
Addition
Half Adder:
A combinational circuit that performs the addition of two bits is called a half adder.
CS6303 – COMPUTER ARCHITECTURE
UNIT-II
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