INDEX

In a fixed point number system, each number has exactly the same number of digits, and the “point” is always in the same place.

Example in decimal → 2.21, 3.56, 1.48

Example in binary → 11.00, 10.00, 00.10

An important difference between the way that we represent fixed point numbers on paper and the way that we represent them in the computer is that when fixed point numbers are represented in the computer the binary point is not stored anywhere , but only assumed to be in a certain position.

RANGE AND PRECISION IN FIXED POINT NUMBERS

A fixed point representation can be characterized by:

• Range of expressible numbers → the distance between the largest and smallest numbers
• Precision → the distance between two adjacent numbers on a number line
• Error → is 1/2 of the difference between two “adjoining” numbers

Example: Using three digits and the decimal point placed two digits from the right (X.XX)

Range → [0.00,9.99]

Precision → 0.01

Error → 0.01/2 = 0.005

Note that → Range and Precision trade off

There is no reason why the range must begin with 0

Range and precision are important issues in computer architecture because both are finite in the implementation of the architecture, but are infinite in the real world, and so the user must be aware of the limitations of trying to represent external information in internal form.

THE ASSOCIATIVE LAW OF ALGEBRA DOES NOT ALWAYS HOLD

IN COMPUTERS