Essentials of Computer Organization and Architecture
Essentials of Computer Organization and Architecture
5th Edition
ISBN: 9781284123036
Author: Linda Null
Publisher: Jones & Bartlett Learning
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Chapter 2, Problem 11E

a)

Explanation of Solution

Converting “100001.111” to decimal equivalent:

Step 1: First separate the given binary fractions into two parts, left binary part and right binary fractions.

Step 2: To convert the binary fraction into decimal number, multiply the left part of the binary number with the positive integers for base 2.

Step 3: Multiply the right part of the binary number with the negative integers for base 2.

Step 4: Add all the values to get the final result.

100001.111     =1x25+0x24+0x23+0x22+0x21+1x20+1x2−1+1x2−2+1x2−3=32+0+0+0+0+1+0.5+0.25+0.125=33.875

Thus, the decimal equivalent of 100001.111 is “33.87510”.

b)

Explanation of Solution

Converting “111111.10011” to decimal equivalent:

Step 1: First separate the given binary fractions into two parts, left binary part and right binary fractions.

Step 2: To convert the binary fraction into decimal number, multiply the left part of the binary number with the positive integers for base 2.

Step 3: Multiply the right part of the binary number with the negative integers for base 2.

Step 4: Add all the values to get the final result.

111111.10011  =1x25+1x24+1x23+1x22+1x21+1x20+1x2−1+0x2−2+0x2−3+1x2−4+1x2−5=32+16+8+4+2+1+0.5+0+0+0.0625+0.03125=63.59375

Thus, the decimal equivalent of 111111.10011 is “63.5937510”.

c)

Explanation of Solution

Converting “1001100.1011” to decimal equivalent:

Step 1: First separate the given binary fractions into two parts, left binary part and right binary fractions.

Step 2: To convert the binary fraction into decimal number, multiply the left part of the binary number with the positive integers for base 2.

Step 3: Multiply the right part of the binary number with the negative integers for base 2.

Step 4: Add all the values to get the final result.

1001100.1011=1x26+0x25+0x24+1x23+1x22+0x21+0x20+1x2−1+0x2−2+1x2−3+1x2−4                        =64+0+0+8+4+0+0+0.5+0+0.125+0.0625                       =76.6875

Thus, the decimal equivalent of 1001100.1011 is “76.687510”.

d)

Explanation of Solution

Converting “10001001.0111” to decimal equivalent:

Step 1: First separate the given binary fractions into two parts, left binary part and right binary fractions.

Step 2: To convert the binary fraction into decimal number, multiply the left part of the binary number with the positive integers for base 2.

Step 3: Multiply the right part of the binary number with the negative integers for base 2.

Step 4: Add all the values to get the final result.

10001001.0111=1x27+0x26+0x25+0x24+1x23+0x22+0x21+1x20+0x2−1+1x2−2+1x2−3+1x2−4                        =128+0+0+0+8+0+0+1+0+0.25+0.125+0.0625                       =137.4375

Thus, the decimal equivalent of 10001001.0111 is “137.437510”.

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Chapter 2 Solutions

Essentials of Computer Organization and Architecture

Ch. 2 - Prob. 1RETCCh. 2 - Prob. 2RETCCh. 2 - Prob. 3RETCCh. 2 - Prob. 4RETCCh. 2 - Prob. 5RETCCh. 2 - Prob. 6RETCCh. 2 - Prob. 7RETCCh. 2 - Prob. 8RETCCh. 2 - Prob. 9RETCCh. 2 - Prob. 10RETC
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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