Книга: Advanced PIC Microcontroller Projects in C

1.22.3 Multiplication and Division of Floating Point Numbers

1.22.3 Multiplication and Division of Floating Point Numbers

Multiplication and division of floating point numbers are rather easy. Here are the steps:

• Add (or subtract) the exponents of the numbers.

• Multiply (or divide) the mantissa of the numbers.

• Correct the exponent.

• Normalize the number.

• The sign of the result is the EXOR of the signs of the two numbers.

Since the exponent is processed twice in the calculations, we have to subtract 127 from the exponent.

An example showing the multiplication of two floating point numbers follows.

Show the decimal numbers 0.5₁₀ and 0.75₁₀ in floating point and then calculate their multiplication.

Convert the numbers into floating point as:

0.510 = 1.0000 ? 2-1

here, s = 0, e – 127 = -1 or e = 126 and f = 0000

or,

0.510 = 0 01110110 (1)000 0000 0000 0000 0000 0000

Similarly,

0.7510 = 1.1000 ? 2-1

here, s = 0, e = 126 and f = 1000

or,

0.7510 = 0 01110110 (1)100 0000 0000 0000 0000 0000

Multiplying the mantissas results in “(1)100 0000 0000 0000 0000 0000.” The sum of the exponents is 126+126=252. Subtracting 127 from the mantissa, we obtain 252–127=125. The EXOR of the signs of the numbers is 0. Thus, the result can be shown in floating point as:

0 01111101 (1)100 0000 0000 0000 0000 0000

This number is equivalent to decimal 0.375 (0.5?0.75=0.375), which is the correct result.

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