# Signed-magnitude Representation

What is Signed-magnitude Representation?

The representation of decimal numbers in everyday business is commonly called the signed-magnitude representation.

In this system, a number consists of a magnitude and a symbol which indicates whether the magnitude is positive or negative.

Thus the decimal numbers + 79, - 82, - 25.2 etc. are interpreted in the usual manner.

This mode of representation can be incorporated to binary numbers quite easily by using an extra bit position to represent the sign. This extra bit is called the SIGN BIT and is placed before the magnitude of the number to be represented. Generally, the MSB is the sign bit and the convention is that when the sign bit is 0, the number represented is positive and when the sign bit is 1, the number is negative.

A few examples of 8-bit signed-magnitude binary numbers along with their decimal equivalents are given below to show the point.

(i) (01101101)2           =           +(109)10

(ii) (11101101)2          =           -(109)10

(iii) (00101011)2         =            +(43)10

(iv) (10101011)2         =            -(43)10

(v) (00000000)2         =             +(0)10

(vi) (10000000)2        =             -(0)10

We note that in signed-magnitude representation two possible representations of zero may be obtained.

• Why Binary Numbers are Used
• Binary to Decimal Conversion
• Conversion of Numbers
• Hexa-decimal Number System
• Conversion of Binary Numbers to Octal or Hexa-decimal Numbers
• Octal and Hexa-Decimal Numbers
• Signed-magnitude Representation
• Arithmetic Operations of Binary Numbers