Arithmetic

18CS34 | COMPUTER ORGANIZATION | Module-4 VTU Notes

VTU | 18CS34 | Module - 4

Arithmetic Operations, Number Representation, and Fast Computation

Arithmetic operations are fundamental to computer systems, involving numbers, characters, and various techniques for efficient computation. This summary covers number representation, arithmetic operations, fast addition and subtraction, multiplication techniques, and integer division.

Numbers and Arithmetic Operations:

Computer systems work with numbers in various forms, including integers, floating-point numbers, and characters. Arithmetic operations involve addition, subtraction, multiplication, and division.

Number Representation:

Number systems like binary, decimal, and hexadecimal are used to represent values. Signed numbers are represented using methods like sign-and-magnitude, one's complement, and two's complement.

Addition and Subtraction of Signed Numbers:

Adding and subtracting signed numbers require considering their representations. Two's complement representation simplifies addition and subtraction, and overflow is detected by checking carry into and out of the sign bit.

Design of Fast Adders:

Fast adders, like carry-lookahead and carry-select adders, optimize addition by reducing the propagation delay associated with carry computation. These adders enhance performance by minimizing critical path delay.

Multiplication of Positive Numbers:

Multiplication involves repeated addition and shifting. Techniques like the shift-and-add method and the Booth algorithm optimize multiplication, reducing the number of operations.

Signed Operand Multiplication and Fast Multiplication:

Multiplying signed numbers requires sign extension and handling the signs of the result. Techniques like Wallace trees and array multipliers expedite multiplication by parallelizing the process.

Integer Division:

Integer division is more complex than multiplication and requires iterative subtraction or other techniques like restoring and non-restoring division algorithms. Division by powers of two is simplified by bit shifting.

Understanding these concepts is essential for efficient arithmetic operations in computer systems. Techniques like fast adders and multiplication algorithms improve computational speed, while proper handling of signed numbers and division ensures accurate results. These principles underpin various applications, from basic calculations to complex mathematical computations, contributing to the overall performance of modern computing systems.