INTRO.TO COMPUTING SYSTEMS >INTL.ED.<
3rd Edition
ISBN: 9781260565911
Author: PATT
Publisher: MCG
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Chapter 2, Problem 19E
Explanation of Solution
To express “-27” into eight-bit 2’s complement number:
- To convert the negative number “-27” into 2’s complement integer,
- First compute the 1’s complement of the corresponding positive number and “1” to that result.
- The positive number for the negative number “-27” is “27”.
- The binary representation of positive number “27” is computed as follows,
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | Integer |
| 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 27 |
- From the above table, the binary representation of positive number “27” in eight bits is “00011011”.
- The 1’s complement of the “00011011” is “11100100”.
- Adding “1” to the above result “11100100” results the value “11100101”.
- The Left most significant Bit (LSB) of the binary number is “1” and it represents the sign of the decimal value is negative.
- Therefore, the 2’s complement number of negative value “-27” in eight-bit is “11100101”.
To express “-27” into sixteen-bit 2’s complement number:
- The 2’s complement number of negative value “-27” is “11100101”...
Explanation of Solution
Explanation with respect to the properties of sign-extension:
- The LSB of the binary number represents the sign of the decimal value.
- The magnitude of positive number does not change by lengthening the sign bit “0” as many bit positions to the left as intended...
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Chapter 2 Solutions
INTRO.TO COMPUTING SYSTEMS >INTL.ED.<
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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