Computer Arithmetic: Floating Point Operations

This lecture covers the basics of computer arithmetic, focusing on floating point numbers. It explains the representation of floating point numbers, including the exponent and significand. The lecture also delves into the conversion of floating point numbers, normalization, and the handling of special cases like zero representation. Additionally, it discusses the dynamic range of floating point numbers and provides examples of floating point arithmetic operations. The lecture concludes with a detailed explanation of a MIPS function for comparing floating point numbers.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related lectures (85)

Related concepts (164)

CS-208: Computer architecture I

The course introduces the students to the basic notions of computer architecture and, in particular, to the choices of the Instruction Set Architecture and to the memory hierarchy of modern systems.

Fixed-point arithmetic

In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals.

IEEE 754

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard.

Floating-point arithmetic

In computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. For example, 12.345 is a floating-point number in base ten with five digits of precision: However, unlike 12.345, 12.3456 is not a floating-point number in base ten with five digits of precision—it needs six digits of precision; the nearest floating-point number with only five digits is 12.

Exponentiation

In mathematics, exponentiation is an operation involving two numbers, the base and the exponent or power. Exponentiation is written as bn, where b is the base and n is the power; this is pronounced as "b (raised) to the (power of) n". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: The exponent is usually shown as a superscript to the right of the base.

Decimal floating point

Decimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal (base-10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial information) and binary (base-2) fractions. The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values.

Computer Arithmetic: Floating Point Numbers CS-208: Computer architecture I

Explores computer arithmetic, emphasizing fixed-point and floating-point numbers, IEEE 754 standard, dynamic range, and floating-point operations in MIPS architecture.

Computer Arithmetic (Integers)CS-208: Computer architecture I

Covers binary representation, two's complement, overflow detection, and operations in MIPS for computer arithmetic with integers.

Arrays in C: Basics and Memory Management

Covers the basics of arrays in C, bitwise operations, file handling, and memory management.

Floating Point Numbers: Representation and Errors CS-119(c): Information, Computation, Communication

Explores the representation of floating point numbers and the impact of errors in numerical computations.

Memory Management in C ME-213: Programmation pour ingénieur

Covers memory allocation, arrays, bitwise operations, and file handling in C programming.