Fixed Point Arithmetic

Fixed point numbers shall be represented using following number systems

• Unsigned Numbers
• Two's Complement.
• One's Complement.
• Signed Magnitude
• Diminished by one
• Signed Digit
• Logarithmic
• Residue Number Systems.

Unsigned Numbers

Using unsigned number system we can represent only positive numbers. If the number is represented using 'N' bit then we can represent the numbers in the range 0 to 2^N-1.

Example:

Let us consider N=8.

Binary representation is given by: 11001010

Decimal representation of above Binary is given by: 202

Two's Complement

Using Two's complement method we can represent both positive and negative numbers(signed integers).If the number is represented using 'N' bit then we can represent the numbers in the range -2^N-1 to 2^N-1-1.

Example:

Let us consider N=8.

Binary representation is given by: 11111000

Decimal representation of above Binary is given by: -8