Computer Architecture # 03 : Arithmetic: HIGH PERFORMANCE ADDITION (13)

3.5.1 HIGH PERFORMANCE ADDITION

The ripple-carry adder that we reviewed in Section 3.2.2  may introduce too much delay into a system. The longest path through the adder is from the inputs of the least significant full adder to the outputs of the most significant full adder.

The process of summing the inputs at each bit position is relatively fast (a small two-level circuit suffices) but the carry propagation takes a long time to work its way through the circuit. In fact, the propagation time is proportional to the number of bits in the operands. This is unfortunate, since more significant figures in an addition translates to more time to perform the addition.

Computer Architecture # 03 : Arithmetic:HIGH PERFORMANCE ARITHMETIC (12)

3.5 HIGH PERFORMANCE ARITHMETIC
For many applications, the speed of arithmetic operations are the bottleneck to performance. Most supercomputers, such as the Cray, the Tera, and the Intel Hypercube are considered “super” because they excel at performing fixed and floating point arithmetic. In this section we discuss a number of ways to improve the speed of addition, subtraction, multiplication, and division.

Computer Architecture # 03 : Arithmetic:FLOATING POINT MULTIPLICATION AND DIVISION (12)

3.4.2 FLOATING POINT MULTIPLICATION AND DIVISION

Floating point multiplication and division are performed in a manner similar to floating point addition and subtraction, except that the sign, exponent, and fraction of the result can be computed separately. If the operands have the same sign, then the sign of the result is positive. Unlike signs produce a negative result. The exponent of the result before normalization is obtained by adding the exponents of the source operands for multiplication, or by subtracting the divisor exponent from the dividend exponent for division. The fractions are multiplied or divided according to the operation, followed by normalization.