Number System Converter

Binary, Decimal, Octal & Hexadecimal — the complete converter

This tool converts any whole number between the four number systems that matter in computing — binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — and updates all four fields the instant you type. Unlike a plain converter that just spits out an answer, it also shows the step-by-step working for each conversion, so it doubles as a study aid when you need to reproduce the method by hand in an exam or lab viva.

How number system conversion actually works

Every number system is a positional system: each digit's value depends on its place, and each place is a power of the base. In decimal, 352 means 3×10² + 5×10¹ + 2×10⁰. The same logic drives every other base — only the base changes. Understanding that one idea lets you convert in any direction without memorising separate rules.

Any base → decimal: multiply each digit by its place value (base raised to the position, counting from 0 on the right) and add them up.

Decimal → any base: divide repeatedly by the target base, keep each remainder, then read the remainders bottom to top.

The shortcut between binary and hex (or octal): you never need decimal as a middle step. Group binary digits into nibbles of 4 for hex, or groups of 3 for octal, from the right. Each group maps to a single hex/octal digit.

Who this converter is for

It's built for the everyday base-conversion moments in Indian tech education and work:

• Engineering & BCA/MCA students revising Digital Electronics, Computer Organization & Architecture (COA), or Microprocessors — the step-by-step view mirrors how conversions are marked in university semester papers and GATE.
• Web developers translating hex colour codes like #16A34A into RGB, or decoding hex values in APIs and config files.
• System administrators reading and setting Linux/Unix file permissions, which are written in octal (chmod 755).
• Embedded & IoT developers working with register masks, bit flags, and memory addresses that are almost always written in hex.

Common mistakes and edge cases

• Reading remainders top-down. The single most common exam error. In repeated division, the first remainder is the least significant bit — always read the column bottom to top.
• Dropping leading zeros in nibbles. When grouping binary into hex, pad the left-most group to a full 4 bits. 101111 is 0010 1111 = 2F, not 101111 read as two loose chunks.
• Hex letter case. ff, Ff and FF are the same value; case is cosmetic. This tool accepts either and outputs uppercase by convention.
• Confusing octal with decimal. In octal there is no digit 8 or 9. If a "number" contains an 8, it isn't valid octal — a frequent slip when reading chmod values.
• Negative numbers. This converter handles unsigned whole numbers. Computers store negatives using two's complement: to get −5 in 8-bit, take 5 (00000101), invert every bit (11111010), add 1 (11111011). That bit pattern reads as 251 if you treat it as unsigned — which is exactly why signed and unsigned interpretations of the same bits differ.
• Fractions. Base conversion of decimals (e.g. 0.625 → binary) uses repeated multiplication, not division, and is a separate method — this tool focuses on integers, the case that covers the vast majority of coursework and dev work.

Frequently asked questions