Information Technology Reference
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Exponent E2
Exponent E1
Mantissa M2
Mantissa M1
Add
Multiply
Result normalization and round logic
Result Exponent
Result Mantissa
Figure 4.14 FP multiplication
Multiplication of two FP numbers can be illustrated using the schematic shown in
Figure 4.14.
Division of a pair of FP numbers X ¼ m x * 2 a and Y ¼ m y * 2 b is
represented as X = Y ¼
Division
(m x = m y ) * 2 a b .
A general algorithm for division of FP numbers consists of three basic steps:
1. Compute the exponent of the result by subtracting the exponents.
2. Divide the mantissa and determine the sign of the result.
3. Normalize and round the resulting value, if necessary.
1.0000 * 2 2 2 and
Example
Consider the division of the two FP numbers X ¼
1.0100 * 2 2 1 .
Y ¼ 2
1. Subtract exponents:
2
(
1)
1.
2
2
2
¼ 2
2. Divide the mantissas: 1.0000
1.0100
0.1101.
42
¼ 2
0.1101 * 2 2 1 .
3. The result is
2
Division of two FP numbers can be illustrated using the schematic shown in
Figure 4.15.
4.3.3. The IEEE Floating-Point Standard
There are essentially two IEEE standard floating-point formats. These are the basic
and the extended formats. In each of these, IEEE defines two formats, that is, the
single-precision and the double-precision formats. The single-precision format is
32-bit and the double-precision is 64-bit. The single extended format should have
at least 44 bits and the double extended format should have at least 80 bits.
 
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