Chapter 2, Problem 30E

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.

Excess-M representation:

To get the excess-M representation of a given number,

• Add the given number with the M
• Convert the obtained value to the binary representation