Essentials of Computer Organization and Architecture
Essentials of Computer Organization and Architecture
5th Edition
ISBN: 9781284123036
Author: Linda Null
Publisher: Jones & Bartlett Learning
Question
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Chapter 2, Problem 26E

26E

Program Plan Intro

Signed magnitude representation:

In signed magnitude representation, an extra bit is used to represent the sign of the number. This extra bit is called sign bit.

  • The Most Significant Bit (MSB) in the binary number is referred as sign bit.
  • In the signed magnitude representation, if the MSB is 0 it is treated as positive sign and if the MSB is 1 it is treated as negative sign.

For example:

Consider the decimal number 36 and can be represented as 00100100 and the -36 can be represented as 10100100.

One’s complement:

The binary numbers can be represented using one’s complement. Here, the value of every binary digit is complemented that is if the value is 1, it becomes 0 and if the value is 0 it becomes 1.

For example:

Consider the binary number 1101, the one’s complement of the given number is 0010.

Two’s complement:

Two’s complement is another way of representing the binary numbers. To implement the two’s complement to the number, the given binary number should be one’s complemented and then add 1 to the result obtained after one’s complement.

For example:

Consider the binary number 1011. First implement the one’s complement to the given binary number. The number becomes 0100. Then add 1 to the resultant obtained after the one’s complement. The result becomes 0101.

a)

Explanation of Solution

Generalizing the range of values using signed magnitude representation:

Generalizing the range of value represented in any given “x” numbers of bits derived from the given two tables using signed magnitude is shown below:

For the number of bits “3” or ...

b)

Explanation of Solution

Generalizing the range of values using one’s complement:

Generalizing the range of value represented in any given “x” numbers of bits from the above given two table represented using one’s complement is shown below:

For the number of bits “3” or...

c)

Explanation of Solution

Generalizing the range of values using two’s complement:

Generalizing the range of value represented in any given “x” numbers of bits from the above given two table represented using two’s complement is shown below:

For the number of bits “3” o...

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Chapter 2 Solutions

Essentials of Computer Organization and Architecture

Ch. 2 - Prob. 11RETCCh. 2 - Prob. 12RETCCh. 2 - Prob. 13RETCCh. 2 - Prob. 14RETCCh. 2 - Prob. 15RETCCh. 2 - Prob. 16RETCCh. 2 - Prob. 17RETCCh. 2 - Prob. 18RETCCh. 2 - Prob. 19RETCCh. 2 - Prob. 20RETCCh. 2 - Prob. 21RETCCh. 2 - Prob. 22RETCCh. 2 - Prob. 23RETCCh. 2 - Prob. 24RETCCh. 2 - Prob. 25RETCCh. 2 - Prob. 26RETCCh. 2 - Prob. 27RETCCh. 2 - Prob. 28RETCCh. 2 - Prob. 29RETCCh. 2 - Prob. 30RETCCh. 2 - Prob. 31RETCCh. 2 - Prob. 32RETCCh. 2 - Prob. 33RETCCh. 2 - Prob. 34RETCCh. 2 - Prob. 1ECh. 2 - Prob. 2ECh. 2 - Prob. 3ECh. 2 - Prob. 4ECh. 2 - Prob. 5ECh. 2 - Prob. 6ECh. 2 - Prob. 7ECh. 2 - Prob. 8ECh. 2 - Prob. 9ECh. 2 - Prob. 10ECh. 2 - Prob. 11ECh. 2 - Prob. 12ECh. 2 - Prob. 13ECh. 2 - Prob. 14ECh. 2 - Prob. 15ECh. 2 - Prob. 16ECh. 2 - Prob. 17ECh. 2 - Prob. 18ECh. 2 - Prob. 19ECh. 2 - Prob. 20ECh. 2 - Prob. 21ECh. 2 - Prob. 22ECh. 2 - Prob. 23ECh. 2 - Prob. 24ECh. 2 - Prob. 25ECh. 2 - Prob. 26ECh. 2 - Prob. 27ECh. 2 - Prob. 29ECh. 2 - Prob. 30ECh. 2 - Prob. 31ECh. 2 - Prob. 32ECh. 2 - Prob. 33ECh. 2 - Prob. 34ECh. 2 - Prob. 35ECh. 2 - Prob. 36ECh. 2 - Prob. 37ECh. 2 - Prob. 38ECh. 2 - Prob. 39ECh. 2 - Prob. 40ECh. 2 - Prob. 41ECh. 2 - Prob. 42ECh. 2 - Prob. 43ECh. 2 - Prob. 44ECh. 2 - Prob. 45ECh. 2 - Prob. 46ECh. 2 - Prob. 47ECh. 2 - Prob. 48ECh. 2 - Prob. 49ECh. 2 - Prob. 50ECh. 2 - Prob. 51ECh. 2 - Prob. 52ECh. 2 - Prob. 53ECh. 2 - Prob. 54ECh. 2 - Prob. 55ECh. 2 - Prob. 56ECh. 2 - Prob. 57ECh. 2 - Prob. 58ECh. 2 - Prob. 59ECh. 2 - Prob. 60ECh. 2 - Prob. 61ECh. 2 - Prob. 62ECh. 2 - Prob. 63ECh. 2 - Prob. 64ECh. 2 - Prob. 65ECh. 2 - Prob. 66ECh. 2 - Prob. 67ECh. 2 - Prob. 68ECh. 2 - Prob. 69ECh. 2 - Prob. 70ECh. 2 - Prob. 71ECh. 2 - Prob. 72ECh. 2 - Prob. 73ECh. 2 - Prob. 74ECh. 2 - Prob. 75ECh. 2 - Prob. 76ECh. 2 - Prob. 77ECh. 2 - Prob. 78ECh. 2 - Prob. 79ECh. 2 - Prob. 80ECh. 2 - Prob. 81ECh. 2 - Prob. 82E
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