Binary floating-point number range, Computer Engineering

Assignment Help:

Q. Binary floating-point number range?

Smallest Negative number

  Maximum mantissa and maximum exponent

    =    - (1 -2-24) × 2127

 Largest negative number

  Minimum mantissa and Minimum exponent

    = -0.5 × 2-128

 Smallest positive number 

    = 0.5 × 2-128

Largest positive number

    = (1 -2-24) × 2127

398_Binary floating-point number range.png

Figure: Binary floating-point number range for given 32 bit format

In floating point numbers basic transaction is between range of numbers and accuracy also known as precision of numbers. If we raise exponent bits in 32-bit format then range can be increased but accuracy of numbers would go down as size of mantissa would become smaller. Let's have an illustration that will elucidate term precision. Suppose we have one bit binary mantissa then we would be able to represent only 0.10 and 0.11 in normalised form as provided in above illustration (having an implicit 1). Values like 0.101, 0.1011 and so on can't be represented like complete numbers. Either they have to be estimated or truncated and would be represented as either 0.10 or 0.11. So it will produce a truncation or round off error. The higher the number of bits in mantissa better would be precision.

In case of floating point numbers for raising both precision and range more bits are required. This can be obtained by employing double precision numbers. A double precision format is generally of 64 bits.

Institute of Electrical and Electronics Engineers (IEEE) is a group that has created many standards in aspect of various aspects of computer has created IEEE standard 754 for floating-point representation and arithmetic. Fundamental aim of developing this standard was to facilitate portability of programs from one to another computer. This standard has resulted in growth of standard numerical capabilities in different microprocessors. This representation is displayed in figure below.

2060_Binary floating-point number range1.png

Figure: IEEE Standard 754 format


Related Discussions:- Binary floating-point number range

What are set up time & hold time constraints, What do they signify Which on...

What do they signify Which one is critical for calculating maximum clock frequency of a circuit? Ans) Set up time constraint implies how late the input signal can arrive befor

What is called when a star connected intermediate exchange, A star connecte...

A star connected intermediate exchange is known as a? A star connected intermediate exchange is termed as a Hub exchange.

Write short note on quantization, Write short note on Quantization. Qua...

Write short note on Quantization. Quantization: This is the first step in PCM. The whole amplitude range of the modulating signal is divided in a number of standard levels term

Generalization-specialization(DBMS), Design a generalization-specialization...

Design a generalization-specialization hierarchy for a motor vehicle sales company. The company sells motorcyles,passenger cars,vans,and buses.justify your placement of attributes

Complex micro-controller, The 68Hc11 is actually a complex micro-controller...

The 68Hc11 is actually a complex micro-controller its contains internally RAM, EEPROM, Parallel IO and serial ports, hardware timers and a 8 channel ADC.  The internal structure is

Disadvantages of stateful multi-layer inspection, Disadvantages of Stateful...

Disadvantages of Stateful Multi-Layer Inspection A firewall such as the SMLI remains completely transparent to both users and applications. Consequently, SMLI firewall does no

Design a sequential circuit with two flip-flop and one input, Design a coun...

Design a counter modulo 4 (sequential circuit with two flip-flops and one input U) which work like that: 1. When U=0, the state of the flip-flop does not change. 2. Whe

What is an html tag, An HTML tag is a syntactical construct in the HTML lan...

An HTML tag is a syntactical construct in the HTML language that abbreviates particular instructions to be implemented when the HTML script is loaded into a Web browser. It is like

Explain essential properties of distributed operating system, Describe the ...

Describe the essential properties of the Distributed Operating System Essential properties of Distributed operating systems: Sharing resources Calculation speed-up

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd