4 Data Representation

4.5 Fixed Point Binary Numbers

4.5.1 Positive Fixed Point Binary Numbers

In binary we can have functional column headings.

27	26	25	24	23	22	21	20		2-1	2-2
128	64	32	16	8	4	2	1		0.5	0.25
1	0	1	0	0	1	0	0	.	1	1
=164.75

Binary Fraction	Fraction	Decimal
0.1	1/2	0.5
0.01	1/4	0.25
0.001	1/8	0.125
0.0001	1/16	0.0625

4.5.2 Using Two's Complement With Fixed Point Binary Numbers

For negative numbers we use two's complement representation on the entire bit pattern.

Example

Represent -5.25₁₀ in 8-bit binary with the binary point after the fourth digit.

Step 1 Calculate the positive equivalent number in binary.				5	.	2	5
	0	1	0	1	.	0	1	0	0
Step 2 Change 0s to 1s and 1s to 0s (Complement).	1	0	1	0	.	1	0	1	1
Step 3 Add 1 to the result.	1	0	1	0	.	1	1	0	0

Advantages And Disadvantages Of The Fixed Point Binary System

Advantages

• Preserves accuracy as required.
• Easy to convert.

Disadvantages

• Limited degree of accuracy.

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