Gate Flop

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

Before designing FPGA arithmatic blocks first we need to decide on number representation. There are two types of number representation is possible in the FPGA. Fixed point representation. Floating point representation. After we decide the number representation, we need to focus on designing the multipliers, adders and arithmetic operators. Fixed Point Representation  Advantage of fixed point implementation is high speed and lower cost. Floating Point Representation  Floating point representation has high dynamic range and also it eliminates the scaling.