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

Illustration of a memory organization, Q. Illustration of a memory organiza...

Q. Illustration of a memory organization? Let's consider an illustration of a memory organization as displayed in Figure below in that main memory can store 32K words of 12 b

Explain digital signatures, Digital Signatures. A digital signature is ...

Digital Signatures. A digital signature is an electronic rather than a written signature that can be used by someone to validate the uniqueness of the sender of a message or of

What are the general security issues, What are the General Security Issues ...

What are the General Security Issues Many issues exist when linking a computer system to the Internet or indeed to an external link via a network set up. There are numerous way

Multiple instruction and multiple data stream (mimd), Multiple Instruction ...

Multiple Instruction and Multiple Data stream (MIMD): In this categorization, numerous processing elements and multiple control units are ordered as in MISD. However the differ

Differentiate between intranet and internet, Differentiate between intranet...

Differentiate between intranet and internet Some comparisons between intranet and internet include: -  INTERNET is INTERnational NETwork -  An INTRANET is INTernal Restri

Illustrate internal organisation of ram, Q. Illustrate Internal Organisatio...

Q. Illustrate Internal Organisation of RAM? The construction displayed in Figure below is made up of one JK flip-flop and 3 AND gates. The two inputs to system are one input bi

Branding choices, Develop a web traffic plan - suppose that there is no/min...

Develop a web traffic plan - suppose that there is no/minimal advertising budget so you will require to look at branding choices & site design, word-of-mouth and publicity as your

Explain a scheme of capability list to implement protection, Describe the s...

Describe the scheme of capability lists to implement protection? Capability lists (C- lists): These lists are utilized to make sure that uses only access files that are e

Describe the lists used in html, Q. Describe the LISTS used in html? Li...

Q. Describe the LISTS used in html? Lists are used when data are to be mentioned in form of points such as: causes of a particular issue, list of items etc. Lists break up mono

What qualifications needs to be an security professionals, Qualifications o...

Qualifications of security professionals For the security professionals, it is essential that they have adequate freedom to check the security measures and enforce them and

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