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 different queues used, 1.Local queue -is a actual queue 2.Clus...

1.Local queue -is a actual queue 2.Cluster queue -is a local queue that is called as throughout a cluster of queue managers 3. Remote queue -structure explaining a queue

Elements of composition, The Elements of composition are the formal languag...

The Elements of composition are the formal language used to communicate in the visual arts. The elements of composition can be loosely broken into 5 main elements, Line, shape, val

Determine resources, Consider the following system snapshot using data stru...

Consider the following system snapshot using data structures in the Banker's algorithm, with resources A, B, C, and D, and process P0 to P4:                           Max

Explain csmsginterface() function with predefined protocol, Explain CSMsgIn...

Explain CSMsgInterface() Function with Predefined Protocol  A REQUEST structure is created for each message sent to the server. Messages passed to CSMsgInterface() as *dataMSG

Iscuss the various functions of telephone switching systems, Discuss the va...

Discuss the various functions of telephone switching systems. Telephone switching system's functions are as follows: (i) Attending: The system should be continually monito

How can we access the correction and transport system, How can we access th...

How can we access the correction and transport system? Each time you make a new object or change an existing object in the ABAP/4 Dictionary, you branch automatically to the W

How dreamweaver work in layout view, Q. How Dreamweaver Work in Layout View...

Q. How Dreamweaver Work in Layout View? Dreamweaver has two visual design views-Standard view and Layout view. You will start by working in Layout view, which allows you to dra

Signalling connection control part and message transfer part, The Signallin...

The Signalling connection control part (SCCP) and message transfer part (MTP) together are referred to as (A) Signal Switching Points (SSPs) (B)  Signal Transfer Points

What is the task of the pass 2 in a two-pass assembler, In a two-pass assem...

In a two-pass assembler, the task of the Pass II is to? Ans. The task of the Pass II is to synthesize the target program in a two-pass assembler.

What are the server specific middle wares, What are the server specific mid...

What are the server specific middle wares? Server specific middle wares. Their role in e-commerce. Additional features needed by e-commerce server. Middleware is the term of

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