Number Systems | Computer for GCSE/IGCSE - Year 11 PDF Download

Introduction

• In the realm of Computer Science, data can be represented using three primary numbering systems: Denary, Binary, and Hexadecimal.

The Denary Number System

• The denary, or decimal, system operates on a base-10 model, employing ten digits from 0 to 9.
• Denary numbers are versatile, capable of representing integers, fractions, and decimal figures.
• In denary notation, each digit's position denotes a power of 10, starting from the rightmost digit representing 100, the next 101, and so forth.
• Converting data between different numerical systems, such as denary to binary or denary to hexadecimal, is a common requirement.
• Conversion processes are greatly facilitated with the aid of a conversion table, streamlining operations. For instance, the number 3268 can be transcribed as follows:
  
• (3 x 1000) + (2 x 100) + (6 x 10) + (8 x 1) = 3268

The Binary Number System

• Binary, a base-2 numbering system, employs just two digits: 0 and 1.
• In binary notation, every digit symbolizes a power of 2, starting from the rightmost digit representing 20, followed by 21, and so forth.
• For instance, the decimal number 12 is represented as 1100 in binary:
  
• We know this as (1 x 8) + (1 x 4) + (0 x 2) + (0 x 1) =12

The Hexadecimal Number System

• Hexadecimal, a base-16 numbering system, incorporates 16 digits: 0 to 9 and A to F, where A represents 10, B represents 11, and so forth up to F, representing 15.
• In hexadecimal notation, each digit signifies a power of 16, with the rightmost digit representing 160, followed by 161, and so forth.
• For example, the decimal number 146 is represented as 92 in hexadecimal: