Binary Numbers

Addition and Subtraction of Binary Numbers using sign bit:

Sometimes an underscore (-) is used to distinguish the sign bit from the magnitude bit.

Thus, if a computer is capable of handling numbers of 5 bits (**i.e.,** sign bit and 4 magnitude bits) then the number - 1011 is represented by __1__1011 where __1__ denotes the negative sign and 1011 is the magnitude of the numbers.

Similarly __0__1101 indicate the binary number + 1101.

A negative numbers may also be represented by using 1’s complement of the magnitude of the number.

Thus the binary number – 1011 may be represented as __1__0100 where the **MSB** __1__ means that the number is negative and 0100 is the 1’s complement of the magnitude of the given number.

Similarly, __1__0011
indicate the number – 1100 and so on.

In the same way 2’s complement may be used to represent a negative binary number.

**For example,** - 1011 may be represented as __1__0101 where __1__
means that the number is negative and 0101 is the 2’s complement of the number
1011.

The addition and subtraction of binary numbers using sign bit methods of representing negative numbers may be used conveniently in the design of computers to evaluate sums and differences of binary numbers by addition only.

- Decimal Number System

- 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

- Radix Complement

- Diminished Radix Complement

- Arithmetic Operations of Binary Numbers

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