U. Glaeser

FIGURE 9.18 Floating-point addition.
Floating-Point Multiplication
The algorithm for floating-point multiplication forms the product of the operand significands and the
sum of the operand exponents. For radix 2 floating point numbers, the significand values are greater
than or equal to 1 and less than 2. The product of two such numbers will be greater than or equal to 1
and less than 4. At most a single right shift is required to normalize the product.
Floating-Point Division
The algorithm for floating-point division forms the quotient of the operand significands and the difference
of the operand exponents. The quotient of two normalized significands will be greater than or equal
to .5 and less than 2. At most a single left shift is required to normalize the quotient.
Floating-Point Rounding
All floating-point algorithms may require rounding to produce a result in the correct format. A variety
of alternative rounding schemes have been developed for specific applications. Round to nearest, round
toward ∞, round toward −∞, and round toward ZERO are required for implementations of the IEEE
floating point standard. Selection should be based on both static and dynamic performance [24], although
round to nearest is appropriate for most applications.
Conclusions
This chapter section has presented an overview of the two’s complement number system, algorithms for the
basic integer arithmetic operations of addition, subtraction, multiplication, and division, and a brief discussion
of floating point operations. When implementing arithmetic units there is often an opportunity
to optimize the performance and the complexity to the requirements of the specific application. In general,
© 2002 by CRC Press LLC
3. S a = S a 2 (E a - E b)
E s = E b
S = ZERO
11. S s = 2S s
E s = E s -1
UNDERFLOW
LT
EQ
LT
LE
1.
E a : E b
EQ
2. E s = E a
5. S s = S a + S b
6.
S s : 2
LT
9.
S s : 0
NE
10.
S s : 1
GE
12.
E s : -127
GT
GE
GT
4. S b = S b 2 (E b - E a)
E s = E a
7. S s = S s /2
E s = E s +1
8.
E s : 128
LT
S = A + B
GE
OVERFLOW