Computer Number Systems — Binary, Octal, Decimal & Hex

Overview

Computers manipulate binary data internally, but humans prefer decimal for arithmetic and hexadecimal for compact binary display. Octal persists in Unix permissions. Understanding when each base appears — and how to convert between them — is essential for programming, debugging, and systems administration.

Binary in Hardware

CPU registers, RAM cells, and bus lines carry voltage levels interpreted as 0 or 1. Instruction opcodes, character codes, and pixel RGB channels all serialize to bit patterns.

Decimal for Humans

User interfaces, financial reports, and most API inputs use decimal strings. Programs convert decimal input to binary internally via parsing algorithms (parseInt, Integer.parseInt, etc.).

Hexadecimal in Development

Debuggers show memory in hex. CSS colours: #FF5733. MAC addresses use hex pairs. IPv6 addresses use hex groups. One hex digit = four bits — the perfect shorthand.

Octal in Unix

chmod 644 = rw-r—r—. Each permission digit is octal. See Octal Conversion Guide.

ASCII and Character Codes

Text is stored as numeric codes. ASCII ‘A’ = 65. Unicode extends this globally. ASCII Converter | ASCII Table

BCD in Legacy Systems

Financial hardware sometimes uses Binary Coded Decimal for exact decimal digits. BCD Explained

Floating Point

Real numbers use IEEE 754 — sign, exponent, mantissa. Not all decimals are exact. IEEE 754 Guide

Study Path

1. Read Number System Guide
2. Practice with Number System Converter
3. Deep dive Binary Number System

Frequently Asked Questions

Which base do programmers use most?

Write decimal, debug hex, think binary for bitwise ops.

Why not one universal base?

Different bases optimise for human readability vs hardware efficiency.

What base is JSON numbers?

Decimal text representation — parsed to binary float/int internally.

How are negative numbers stored?

Two’s complement in most languages (Java, C, Python ints).

Where are all Numverto number tools?

Browse all 13 tools — converters, arithmetic, ASCII, BCD, IEEE 754.