Computer Architecture # 03 : Arithmetic: FLOATING POINT ADDITION AND SUBTRACTION (10)

3.4.1 FLOATING POINT ADDITION AND SUBTRACTION
Floating point arithmetic differs from integer arithmetic in that exponents must be handled as well as the magnitudes of the operands. As in ordinary base 10 arithmetic using scientific notation, the exponents of the operands must be made equal for addition and subtraction. The fractions are then added or subtracted as appropriate, and the result is normalized. 
This process of adjusting the fractional part, and also rounding the result can lead to a loss of precision in the result. Consider the unsigned floating point addition (.101 × 2³ + .111 × 2⁴) in which the fractions have three significant digits. We start by adjusting the smaller exponent to be equal to the larger exponent, and adjusting the fraction accordingly.

Computer Architecture # 03 : Arithmetic: FLOATING POINT ARITHMETIC (10)

 3.4 Floating Point Arithmetic
Arithmetic operations on floating point numbers can be carried out using the fixed point arithmetic operations described in the previous sections, with attention given to maintaining aspects of the floating point representation. In the sections that follow, we explore floating point arithmetic in base 2 and base 10, keeping the requirements of the floating point representation in mind.