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26E
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
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