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

Give brief summary of common aspects found in spreadsheets, Give brief summ...

Give brief summary of common aspects found in spreadsheets -  It's made up of columns and rows; every row is identified by a number and every column is identified with a letter

Determine the frequency of the input signal, An eight stage ripple counter ...

An eight stage ripple counter uses a flip-flop with propagation delay of 75 nanoseconds.  The pulse width of the strobe is 50ns.  The frequency of the input signal which can be use

Nix commands, reate a directory "Unix" under your home directory. Command(...

reate a directory "Unix" under your home directory. Command(s): ………………………………………….

Which of the memory is volatile memory, Which of the memory is volatile mem...

Which of the memory is volatile memory ? Ans. A volatile memory is RAM. Term Volatile memory implies the contents of the RAM get erased as soon as the power goes off.

Difficulties - canonical genetic algorithm, Difficulties - canonical geneti...

Difficulties - canonical genetic algorithm: Therefore the first big problem we face whether designing an "AI" agent to perform a GA-style search is how to represent the soluti

Show basic types of transmission technologies, Q. What are the basic types ...

Q. What are the basic types of Transmission technologies, basis on which computer networks will be categorized? Ans: Broadly there are two kinds of transmission technology:

Data structure, Sort the following list using selection sort technique, dis...

Sort the following list using selection sort technique, displaying each step. 20,12,25,6,10,15,13

Name the two operations of stack, Name the two operations of stack A st...

Name the two operations of stack A stack has only two operations and they are insertion and deletion of items. The operation insertion is called push (or push-down) as it can b

What is multiplicity, What is multiplicity? Multiplicity is applied to ...

What is multiplicity? Multiplicity is applied to attributes for data base application. Multiplicity for an attribute specifies the number of possible value for every instantiat

What is secondary list, What is secondary list? It permits you to enha...

What is secondary list? It permits you to enhance the information presented in the basic list.  The user can, for example, select a line of the basic list for which he require

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