GCSE Link: 3.02 (Binary and Hexadecimal)

Fixed Point Representation is a way of representing fractions in binary.

Have you ever wondered how to store fractions in binary? Well, if we add a decimal point after the number and then a digit after that, this digit now represents a half. Add another digit and it represents a quarter. Then one-eighth, one-sixteenth, and so on. This is called Fixed Point Representation, because the decimal point is always fixed in the same place.

Diagram 1 shows the number 26.625 represented in binary using Fixed Point Representation.

Diagram 1

---

How many bits would be required to store any fraction from -128 to +127 to at least 6 decimal places using Fixed Point Representation?

We would need one bit for the sign, seven bits for the rest of the integer, and 20 bits for the fraction (2-20 = 1/1,048,576). This is a total of 28 bits. This is not very efficient. We'll learn more about floating point representation, a more efficient way of representing fractions, on the next page.

---