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## Precision and Errors

After studying this chapter, you should be able to:

• understand various errors and their sources
• perform precise computations
• write MATLAB® code for accurate results

#### 10.1 Introduction

Though in everyday life, numbers are almost exclusively represented using the base 10 decimal system, computers use a base 2 system, which is called binary system. An integer N is represented in an n-bit system as,

N = (an−1..aj..a1a0 = an−1 × 2n−1 + a1 × 21 + a0 × 20

where ai′s are only 0 or 1. An example of a binary number in an 8-bits system is as follows:

N = (01101101)2 = 0 ×27 + 1 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20

You can determine the binary representation of integers in MATLAB by the command dec2bin ...

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