Introduction To Computing Systems
Introduction To Computing Systems
3rd Edition
ISBN: 9781260150537
Author: PATT, Yale N., Patel, Sanjay J.
Publisher: Mcgraw-hill,
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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,
1286432168421Integer
0001101127
  • 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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