Types of representation for signed number: Signed magnitude representation One’s complement Two’s complement Excess-M representation 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.

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Chapter 2, Problem 27E

Program Plan Intro

Types of representation for signed number:

Signed magnitude representation

One’s complement

Two’s complement

Excess-M representation

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.

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