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 the differences between struts and units, What are the differences...

What are the differences between struts and units?  A warm up question. Units are static objects that exist from the start of the simulation right up to its end, whereas struts

Struct and class, https://dl.dropbox.com/u/41918180/Images/Pro%202/2.png ...

https://dl.dropbox.com/u/41918180/Images/Pro%202/2.png https://dl.dropbox.com/u/41918180/Images/Pro%202/3.png https://dl.dropbox.com/u/41918180/Images/Pro%202/4.png">https://dl.d

First-order logic - artificial intelligence, First-Order Logic : There'...

First-Order Logic : There's Reasoning, and then There's Reasoning As humans, we have always prided ourselves on our capability to think things by: to reason things out and c

Explain about the term false path, Explain about the term false path? How i...

Explain about the term false path? How it find out in circuit? What the effect of false path in circuit? By timing all the paths into the circuit the timing analyzer can find o

Forall statement in fortran, Q. FORALL Statement in fortran? The FORALL...

Q. FORALL Statement in fortran? The FORALL statement permits for more common assignments to sections of an array. A FORALL statement has general form.   FORALL ( triplet, ..

C++, A palindrome is a string that reads the same from both the ends. Given...

A palindrome is a string that reads the same from both the ends. Given a string S convert it to a palindrome by doing character replacement. Your task is to convert S to palindrome

Memory cache hierarchy and virtual memory system, 1. Detail for each of the...

1. Detail for each of the four following MIPS instructions, which actions are being taken at each of their five steps. Do not forget to mention how and during which steps each inst

What is sensitivity list, What is sensitivity list? A list of signals w...

What is sensitivity list? A list of signals which trigger execution of the block when they change value. Sensitivity list  indicates that when a change occurs to any one of

Using network drive mappings, If various load generators need to access the...

If various load generators need to access the similar physical files, rather than having to remember to copy the files every time they change, each load generator can reference a c

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