## Friday, March 25, 2011

### Computer Architecture # 02 : Data Representation : Fixed Point Numbers (2)

2.2 Fixed Point Numbers
In a ﬁxed point number system, each number has exactly the same number of digits, and the “point” is always in the same place. Examples from the decimal number system would be 0.23, 5.12, and 9.11. In these examples each number has 3 digits, and the decimal point is located two places from the right. Examples from the binary number system (in which each digit can take on only one of the values: 0 or 1) would be 11.10, 01.10, and 00.11, where there are 4 binary digits and the binary point is in the middle.
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. One could say that the binary point exists only in the mind of the programmer.

We begin coverage of ﬁxed point numbers by investigating the range and precision of ﬁxed point numbers, using the decimal number system. We then take a look at the nature of number bases, such as decimal and binary, and how to convert between the bases. With this foundation, we then investigate several ways of representing negative ﬁxed point numbers, and take a look at simple arithmetic operations that can be performed on them.