Programming in MATLAB ®

10

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 = (a_n−1..a_j..a₁a₀ = a_n−1 × 2ⁿ⁻¹ + a₁ × 2¹ + a₀ × 2⁰

where a_i′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 ...