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 is an identification method, An identification method notifies Robot h...

An identification method notifies Robot how to recognize the values to compare during record and playback.

Isoquants, what are the types of isoquants

what are the types of isoquants

Public key infrastructure solutions, Public Key Infrastructure solutions ...

Public Key Infrastructure solutions The use of public-key based security systems requires great attention and due care in design and management of security features. The secur

When should we stop testing, When should you stop testing? It is quite ...

When should you stop testing? It is quite complex to determine as many modern software applications are so complex and run in like an interdependent environment that complete t

Loop level-levels of parallel processing, Loop Level At this level, rep...

Loop Level At this level, repeated loop iterations are the applicants for parallel execution. However, data dependencies among subsequent iterations may limit parallel executio

linq file extension, What is the LINQ file extension that interacts with C...

What is the LINQ file extension that interacts with Code Behinds objects? Ans) The extension of the file is .dbml

How to use data validation function in vba, Data validation is a significan...

Data validation is a significant concept in VBA. Application process and a custom dialog box can be used to accurate input errors. You can assign an application process to the fram

Explain the term granularity, Granularity Granularity refers to the qua...

Granularity Granularity refers to the quantity of computation done in concurrent relative to the size of whole program. In concurrent computing, granularity is a qualitative me

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