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

Data structure, Process: pid start time end time priority t...

Process: pid start time end time priority timeslice list of CPU bursts list of IO bursts (the number of IO burst will always be 1 less than the number of CPU

Quick sort exhibit its worst-case behaviour, In which input data does the a...

In which input data does the algorithm quick sort exhibit its worst-case Behaviour? The Quick Sort method exhibits its worst-case behavior when the input data is " Already Comp

Determine waiting and average waiting time of CPU, CPU burst time indicates...

CPU burst time indicates the time, the process needs the CPU. The following are the set of processes with their respective CPU burst time     (in milliseconds). Process

Illustrate about object oriented development, Illustrate about object orien...

Illustrate about object oriented development object oriented development is not direct way of system development as in this approach a holistic view of application domain is co

Poor technology or system requirements definition, Poor Technology or Syste...

Poor Technology or System Requirements Definition - Information System Previously we looked at product design and specifically the importance of requirements capture as part o

Rpn procedure, Apply this algorithm to your MASM program 1) Declare the ...

Apply this algorithm to your MASM program 1) Declare the following variables in your data segment: .data ; ; These are the values of the variables ; Variables

What is the application of e-commerce in home shopping, What is the applica...

What is the application of E-Commerce in Home Shopping? Application of E-Commerce in Home Shopping: Television broadcast of goods for purchase sent it directly to a viewe

Project, write a programme to simulate a train station to automate

write a programme to simulate a train station to automate

Communications between r/3 and external applications, What is the means of ...

What is the means of communications between R/3 and external applications? The means of communication among R/2,R/3 and external applications is by the CPI-C handler or SAP Gat

Perform multiplication with showing content of accumulator, Perform multipl...

Perform multiplication with showing the contents of accumulator, B register and Y register during each step. (Accumulator, B, Y are 4-bit registers) B=06 Y=02

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