Texas Instruments TMS320C3x 사용자 설명서

Floating-Point Addition and Subtraction

5-35

Data Formats and Floating-Point Operation

Example 5–14.  Floating-Point Subtraction

A subtraction is performed in this example. Let:

α

= 01.0000000000000000000000000000001 

×

  2

0

b = 01.0000000000000000000000000000000  

×

  2

0

The operation performed is 

α

–

b. The mantissas are already aligned because

the two numbers have the same exponent. The result is a large cancellation
of the upper bits, as shown below.

01.0000000000000000000000000000001 

×

 2

0

–01.0000000000000000000000000000000  

×

 2

0

00.0000000000000000000000000000001 

×

 2

0

The result must be normalized. In this case, a left shift of 31 is required. The
exponent of the result is modified accordingly. The result is:

01.0000000000000000000000000000001 

×

 2

0

– 01.0000000000000000000000000000000  

×

 2

0

01.0000000000000000000000000000000

×

2

–31

Example 5–15.  Floating-Point Addition With a 32-Bit Shift

This example illustrates a situation where a full 32-bit shift is necessary to
normalize the result. Let:

α

= 01.1111111111111111111111111111111 

×

  2

127

b = 10.0000000000000000000000000000000  

×

  2

127

The operation to be performed is 

α

 + 

b.

01.1111111111111111111111111111111 

×

  2

127

+ 10.0000000000000000000000000000000  

×

  2

127

11.1111111111111111111111111111111 

×

  2

127

Normalizing the result requires a left shift of 32 and a subtraction of 32 from
the exponent. The result is:

01.1111111111111111111111111111111 

×

  2

127

+ 10.0000000000000000000000000000000  

×

  2

127

11.1111111111111111111111111111111 

×

  2

127