EBK COMPUTER SYSTEMS
EBK COMPUTER SYSTEMS
3rd Edition
ISBN: 8220101459107
Author: O'HALLARON
Publisher: YUZU
Question
Book Icon
Chapter 2, Problem 2.85HW

A.

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 define 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 denoted by “E”. Its weights the value by a power of 2.

In floating-point representation, the bit is denoted 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.

      EBK COMPUTER SYSTEMS, Chapter 2, Problem 2.85HW , 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.

      EBK COMPUTER SYSTEMS, Chapter 2, Problem 2.85HW , 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 formula for 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 formula for significand “M” is “1 + f”.

      EBK COMPUTER SYSTEMS, Chapter 2, Problem 2.85HW , additional homework tip  3

  • Case 2: Denormalized value
    • This case occurs when the exponent field is all zeros.
    • The formula for exponent value is “E=1-bias”.
    • Here the formula for significand “M” is “M = f”.

      EBK COMPUTER SYSTEMS, Chapter 2, Problem 2.85HW , 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”.

      EBK COMPUTER SYSTEMS, Chapter 2, Problem 2.85HW , 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”.

EBK COMPUTER SYSTEMS, Chapter 2, Problem 2.85HW , additional homework tip  6

B.

Explanation of Solution

For largest odd integer:

Here, consider “bias >> n”.

Consider the value for the largest odd integer is

  • The value of “M” must be “0b1.1111111....
  • The value of “f” will be “0b0.111111111....” (Here “n” bits “1”)

Then value of “E”, E = n.

Now V = 0b0.111111111....{Here (n + 1) bits 1} which implies 2n+1-1

C.

Explanation of Solution

For reciprocal of the smallest positive normalized value:

From the smallest positive normalized value, the bit for exponent bit and fraction bit is given below:

  • For exponent field, place “1” in the least significant bit and remaining are all zeros. So, exponent becomes “0b1”.
  • For fraction field, all bits are zeros. So, it becomes “0000.....”, it can be represented by “0b0.00000
  • From the normalized case, the formula for “E” and “M” is given below.
    • Computing value of “E” by “E = e – bias”.
      • From the given binary representation “0b1”, decimal value of “e” is “1”.
        • Hence, E = e - bias = 1 - bias
    • Computing value of “M” by “M = 1 + f”.
  • From the given representation “0000.....”, value of “f” is “0”. So, M = 1 + f = 1 + 0 = 1. So, value of “M” is “1” it can be write as “0b1.00000
  • Therefore, the value of “M” must be “0b1.00000” and the value of “f” must be “0b0.00000”.

Now compute the value of “V” by using V = (-1)S × M × 2E

From the given question, the value is in positive. Hence, value of “s” is “0”.

V = (-1)S × M × 2E=(-1)0 × 1 × 21-bias=1

Blurred answer
Students have asked these similar questions
Use the created table as in Question 1, solve the problems as mentioned below. You will have to import the respective CSV files of the above created tables as without them, it is impossible to solve the questions below. If you are not able to upload the files successfully, do not leave the query questions. Just write the query to the best of your knowledge. Do not copy. To be graded for the screenshot answer, you must upload the CSV properly and paste the resulting screenshot of the queries as asked. Look at the sum of profits for each Product Sub-Category. Which sub-category is $31,069 below the average profit across all categories? Write the Query in box below. [4 Marks] Paste the screenshot of a portion of the answer below. [1 Marks Write a query to find the contribution of total Sales by the 'Home Office' Customer Segment in the year 2012? For example, if in 2012, the total sum of sales across all Customer segments is 100 and 'Home Office' contributes 30 to the sum of sales. Then…
Database
Can you help me with this problem

Chapter 2 Solutions

EBK COMPUTER SYSTEMS

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
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Computer Networking: A Top-Down Approach (7th Edi...
Computer Engineering
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:PEARSON
Text book image
Computer Organization and Design MIPS Edition, Fi...
Computer Engineering
ISBN:9780124077263
Author:David A. Patterson, John L. Hennessy
Publisher:Elsevier Science
Text book image
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:9781337569330
Author:Jill West, Tamara Dean, Jean Andrews
Publisher:Cengage Learning
Text book image
Concepts of Database Management
Computer Engineering
ISBN:9781337093422
Author:Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:Cengage Learning
Text book image
Prelude to Programming
Computer Engineering
ISBN:9780133750423
Author:VENIT, Stewart
Publisher:Pearson Education
Text book image
Sc Business Data Communications and Networking, T...
Computer Engineering
ISBN:9781119368830
Author:FITZGERALD
Publisher:WILEY