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 is a virtual address, Q. What is a virtual address? Von Neumann ha...

Q. What is a virtual address? Von Neumann had suggested that execution of a program is possible only if program and data are residing in memory. In such a condition program len

What is software interrupt, What is software interrupt?   A software in...

What is software interrupt?   A software interrupt is initiated by implementing an instruction.  Software interrupt is a special call instruction that behaves like an interrupt

Array of discount rates, Why do you think you are asked to do valuation giv...

Why do you think you are asked to do valuation given an array of discount rates? a.    Would it not be extra accurate to utilize, for intsnces , CAPM to calculate cost of equity

What is managed bean or mbean, A managed bean - sometimes simply referred t...

A managed bean - sometimes simply referred to as an MBean - is a type of JavaBean, developed with dependency injection. Managed Beans are particularly used in the Java Management E

Explain congestion, Explain CONGESTION. CONGESTION: This is uneconomi...

Explain CONGESTION. CONGESTION: This is uneconomic to provide sufficient equipment to carry entire traffic that could possibly be given to a telecommunication system. Inside

What is secondary storage systems, There are various limitations of primary...

There are various limitations of primary memory like limited capacity which is its not enough to store a very large volume of data and volatility which is when power is turned off

Which objects are independent transport objects, Which objects are independ...

Which objects are independent transport objects? Domains, Data elements, Tables, Technical settings for tables, Secondary indexes for transparent tables, Structures, Views, Ma

Find the width of a time division space switch, I n a time division space s...

I n a time division space switch the size of the control memory is N and its Width:  (A) Log 10 M  (B) Log e M  (C) Log N M  (D) Log 2 M Where N are the ou

Describe about frameset, Q. Describe about Frameset? Now make a master ...

Q. Describe about Frameset? Now make a master page in which you write below code. My Frame Page -- The Master Page

naming convention in local scope variables, Description Variables show ...

Description Variables show values that can be changed within a procedure or function. Local scope variables are placeholders that reside within a function- or a script-body.

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