Loose Leaf For Introduction To Computing Systems: From Bits & Gates To C & Beyond
3rd Edition
ISBN: 9781260424744
Author: Yale N. Patt, Sanjay Patel
Publisher: McGraw-Hill Education
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Expert Solution & Answer
Chapter 2, Problem 20E
a.
Explanation of Solution
1100 + 0011:
- The process of addition can perform on “1” digit at a time from right to left.
- A sum digit and a carry digit are generated at each point.
- It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
- The addition of 4-bit 2’s complement binary numbers is as follows,
- Therefore, the resultant binary bit pattern is “1111”.
- The given binary numbers having the opposite sign.
- If the sign bit is “0” then the number is positive.
- If the sign bit is “1”, the number is negative.
- If the user adds the input binary numbers of different sign, then no overflow occurs in the result.
Justification:
- The sign bit of the binary number “1100” is “1” and it indicates that this number is negative.
- The decimal value for the binary number “1100” is “-4”
- The sign bit of the binary number “0011” is “0” and it indicates that this number is positive...
b.
Explanation of Solution
1100 + 0100:
- The process of addition can perform on “1” digit at a time from right to left.
- A sum digit and a carry digit are generated at each point.
- It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
- The addition of 4-bit 2’s complement binary numbers is as follows,
- Therefore, the resultant binary bit pattern is “0000”.
- The given binary numbers having the opposite sign.
- If the sign bit is “0” then the number is positive.
- If the sign bit is “1”, the number is negative.
- If the user adds the input binary numbers of different sign, then no overflow occurs in the result.
Justification:
- The sign bit of the binary number “1100” is “1” and it indicates that this number is negative.
- The decimal value for the binary number “1100” is “-4”
- The sign bit of the binary number “0100” is “0” and it indicates that this number is positive...
c.
Explanation of Solution
0111 + 0001:
- The process of addition can perform on “1” digit at a time from right to left.
- A sum digit and a carry digit are generated at each point.
- It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
- The addition of 4-bit 2’s complement binary numbers is as follows,
- Therefore, the resultant binary bit pattern is “1000”.
- If the sign bit is “0” then the number is positive.
- If the sign bit is “1”, the number is negative.
- The given binary numbers having the same positive sign.
- If the user adds the input binary numbers with same sign, then overflow occurs in the result.
Justification:
- The sign bit of the binary number “0111” is “0” and it indicates that this number is positive.
- The decimal value for the binary number “0111” is “7”.
| 23 | 22 | 21 | 20 | Integer |
| 8 | 4 | 2 | 1 | |
| 0 | 1 | 1 | 1 | 7 |
- The sign bit of the binary number “0001” is “0” and it indicates that this number is positive
d.
Explanation of Solution
1000 – 0001:
- The given operation can also be written as “1000+(-0001)”.
- The process of addition can perform on “1” digit at a time from right to left.
- A sum digit and a carry digit are generated at each point.
- It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
- The 2’s complement of “0001” is “1111”.
- The addition of 4-bit 2’s complement binary numbers is as follows,
- Therefore, the resultant binary bit pattern is “0111”.
- The binary numbers used for addition having the same negative sign.
- If the sign bit is “0” then the number is positive.
- If the sign bit is “1”, the number is negative.
- If the user adds the input binary numbers of same sign, then overflow occurs in the result...
e.
Explanation of Solution
0111 + 1001:
- The process of addition can perform on “1” digit at a time from right to left.
- A sum digit and a carry digit are generated at each point.
- It the user adds “1” and “1”, it generates the sum digit “0” and carry digit “1”.
- The addition of 4-bit 2’s complement binary numbers is as follows,
- Therefore, the resultant binary bit pattern is “0000”.
- The given binary numbers having the opposite sign.
- If the sign bit is “0” then the number is positive.
- If the sign bit is “1”, the number is negative.
- If the user adds the input binary numbers of different sign, then no overflow occurs in the result...
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A
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Chapter 2 Solutions
Loose Leaf For Introduction To Computing Systems: From Bits & Gates To C & Beyond
Ch. 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. 10E
Ch. 2 - Prob. 11ECh. 2 - Prob. 12ECh. 2 - Prob. 13ECh. 2 - Prob. 14ECh. 2 - Prob. 15ECh. 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 - When is the output of an AND operation equal to...Ch. 2 - Prob. 29ECh. 2 - Prob. 30ECh. 2 - When is the output of an OR operation equal to 1?
Ch. 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 - A computer programmer wrote a program that adds...Ch. 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 - Fill in the truth table for the equations given....Ch. 2 - Prob. 55ECh. 2 - Prob. 56E
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