COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG
COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG
3rd Edition
ISBN: 9780134671123
Author: Bryant
Publisher: PEARSON
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Chapter 2.4, Problem 2.52PP
Program Plan Intro

IEEE floating-point representation:

The IEEE floating-point standard denotes a number in a form  V = (-1)S × M × 2E

From the above form,

  • The sign is denoted by “s”. It is used to determine whether the number is in negative or positive.
    • If the number is positive, then “s” is “0”.
    • If the number is negative, then “s” is “1”.
  • The significand is denoted by “M”. It is a fractional binary number.
    • The number ranges either between “1” and “2 - ” or between “0” and “1 - ”.
  • The exponent is represented by “E”. Its weights the value by a power of 2.

In floating-point representation, the bit is represented by three fields such as sign, exponent and fraction field.

  • The single sign bit “s” directly converts the sign
    “s”.
  • The k-bit exponent field exp=ek-1..........e1e0 converts the exponent “E”.
  • The n-bit fraction field frac=fn-1..........f1f0 converts the significant “M”.
  • There are two formats are used for floating-point bit representation. They are “32-bit” format and “64-bit” format.
  • “32-bit” format:
    • It is the single precision format.
    • In this format, “1” bit for sign field, “8” bit for exponent field and “23” bits for fraction field.

      COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG, Chapter 2.4, Problem 2.52PP , additional homework tip  1

  • “64-bit” format:
    • It is the double precision format.
    • In this format, “1” bit for sign field, “11” bit for exponent field and “52” bits for fraction field.

      COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG, Chapter 2.4, Problem 2.52PP , additional homework tip  2

There are three types of cases occurs based on the single precision format. It is occur when the value encoded by a given bit representation can be divided into three different cases.

  • Case 1: Normalized value
    • This case occurs when the bit of “exp” is neither all zeros or nor all ones.
      • Numeric value for all zeros is “0”.
      • Numeric value for all ones is “255”.
    • In this case, the exponent value, E = e – bias.
      • Here, “e” represents unsigned number containing bit representation ek-1..........e1e0 and bias value is 2k-1-1.
    • The fraction field “frac” is interpreted as representing the fractional value “f”.
    • The significand “M” is “1 + f”.

      COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG, Chapter 2.4, Problem 2.52PP , additional homework tip  3

  • Case 2: Denormalized value
    • This case occurs when the exponent field is all zeros.
    • The exponent value is “E = 1 – Bias”.
    • Here the value of significand “M” is “M = f”.

      COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG, Chapter 2.4, Problem 2.52PP , additional homework tip  4

  • Case 3: Special values
    • This case occurs in two formats such as “infinity” and “NaN”.
    • When the exponent field is all ones and the fraction field is all zeros, then the resulting value is represented by “infinity”.

      COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG, Chapter 2.4, Problem 2.52PP , additional homework tip  5

    • When the exponent field is all ones and the fraction field is not all zeros, then the resulting value is represented by “NaN”.

COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG, Chapter 2.4, Problem 2.52PP , additional homework tip  6

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Chapter 2 Solutions

COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG

Ch. 2.1 - Prob. 2.11PPCh. 2.1 - Prob. 2.12PPCh. 2.1 - Prob. 2.13PPCh. 2.1 - Prob. 2.14PPCh. 2.1 - Prob. 2.15PPCh. 2.1 - Prob. 2.16PPCh. 2.2 - Prob. 2.17PPCh. 2.2 - Practice Problem 2.18 (solution page 149) In...Ch. 2.2 - Prob. 2.19PPCh. 2.2 - Prob. 2.20PPCh. 2.2 - Prob. 2.21PPCh. 2.2 - Prob. 2.22PPCh. 2.2 - Prob. 2.23PPCh. 2.2 - Prob. 2.24PPCh. 2.2 - Prob. 2.25PPCh. 2.2 - Practice Problem 2.26 (solution page 151) You are...Ch. 2.3 - Prob. 2.27PPCh. 2.3 - Prob. 2.28PPCh. 2.3 - Prob. 2.29PPCh. 2.3 - Practice Problem 2.30 (solution page 153) Write a...Ch. 2.3 - Prob. 2.31PPCh. 2.3 - Practice Problem 2.32 (solution page 153) You are...Ch. 2.3 - Prob. 2.33PPCh. 2.3 - Prob. 2.34PPCh. 2.3 - Practice Problem 2.35 (solution page 154) You are...Ch. 2.3 - Prob. 2.36PPCh. 2.3 - Practice Problem 2.37 solution page 155 You are...Ch. 2.3 - Prob. 2.38PPCh. 2.3 - Prob. 2.39PPCh. 2.3 - Practice Problem 2.40 (solution page 156) For each...Ch. 2.3 - Prob. 2.41PPCh. 2.3 - Practice Problem 2.42 (solution page 156) Write a...Ch. 2.3 - Practice Problem 2.43 (solution page 157) In the...Ch. 2.3 - Prob. 2.44PPCh. 2.4 - Prob. 2.45PPCh. 2.4 - Prob. 2.46PPCh. 2.4 - Prob. 2.47PPCh. 2.4 - Prob. 2.48PPCh. 2.4 - Prob. 2.49PPCh. 2.4 - Prob. 2.50PPCh. 2.4 - Prob. 2.51PPCh. 2.4 - Prob. 2.52PPCh. 2.4 - Practice Problem 2.53 (solution page 160) Fill in...Ch. 2.4 - Practice Problem 2.54 (solution page 160) Assume...Ch. 2 - Compile and run the sample code that uses...Ch. 2 - Try running the code for show_bytes for different...Ch. 2 - Prob. 2.57HWCh. 2 - Write a procedure is_little_endian that will...Ch. 2 - Prob. 2.59HWCh. 2 - Prob. 2.60HWCh. 2 - Prob. 2.61HWCh. 2 - Write a function int_shifts_are_arithmetic() that...Ch. 2 - Fill in code for the following C functions....Ch. 2 - Write code to implement the following function: /...Ch. 2 - Write code to implement the following function: /...Ch. 2 - Write code to implement the following function: / ...Ch. 2 - You are given the task of writing a procedure...Ch. 2 - Prob. 2.68HWCh. 2 - Write code for a function with the following...Ch. 2 - Write code for the function with the following...Ch. 2 - You just started working for a company that is...Ch. 2 - You are given the task of writing a function that...Ch. 2 - Write code for a function with the following...Ch. 2 - Write a function with the following prototype: /...Ch. 2 - Prob. 2.75HWCh. 2 - The library function calloc has the following...Ch. 2 - Prob. 2.77HWCh. 2 - Write code for a function with the following...Ch. 2 - Prob. 2.79HWCh. 2 - Write code for a function threefourths that, for...Ch. 2 - Prob. 2.81HWCh. 2 - Prob. 2.82HWCh. 2 - Prob. 2.83HWCh. 2 - Prob. 2.84HWCh. 2 - Prob. 2.85HWCh. 2 - Intel-compatible processors also support an...Ch. 2 - Prob. 2.87HWCh. 2 - Prob. 2.88HWCh. 2 - We are running programs on a machine where values...Ch. 2 - You have been assigned the task of writing a C...Ch. 2 - Prob. 2.91HWCh. 2 - Prob. 2.92HWCh. 2 - following the bit-level floating-point coding...Ch. 2 - Following the bit-level floating-point coding...Ch. 2 - Following the bit-level floating-point coding...Ch. 2 - Following the bit-level floating-point coding...Ch. 2 - Prob. 2.97HW
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