Octal Number System

Overview

The octal number system (base-8) uses eight digits (0-7) and serves as a convenient shorthand for binary numbers in digital systems. Each octal digit represents exactly three binary digits, making it easier to read and write long binary numbers. This system was historically important in early computing and is still used in some specialized applications.

Detailed Explanation

Binary to Octal Conversion

Binary:  001 111 010 110
Octal:    1   7   2   6
         (1726 octal)

Conversion Table:
000 = 0    100 = 4
001 = 1    101 = 5
010 = 2    110 = 6
011 = 3    111 = 7

Position Values

Position: 8³  8²  8¹  8⁰
Value:   512  64   8   1

Quick Reference

Octal: 0 1 2 3 4 5 6 7
Binary: 
000 001 010 011 100 101 110 111

Practice Problems

1. Convert to binary:
   • 374₈
   • 652₈
   • 127₈

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