Number Base Converter

Number systems in computing

Computers store and process everything as binary (base 2). But reading long strings of 1s and 0s is error-prone for humans, so we use more compact representations: octal (base 8) and hexadecimal (base 16). Each hex digit maps to exactly 4 binary bits, making the conversion lossless and mental.

Common uses by base

• Binary — CPU instruction sets, bitmasking, flags, network subnet masks
• Octal — Unix file permissions (chmod), some legacy protocols
• Decimal — Human-readable numbers, port numbers, IP addresses
• Hexadecimal — Memory addresses, color codes, SHA hashes, byte sequences, UUID values

Quick conversion reference

Memorizing a few hex-to-binary pairs makes manual conversion much faster: 0=0000, 1=0001, 4=0100, 8=1000, A=1010, F=1111. Any hex value can be converted to binary by simply substituting each hex digit with its 4-bit binary equivalent.

Common use cases for base conversion

Computer science students use base conversion exercises to understand digital logic and low-level programming. Embedded systems engineers convert between hex and binary when reading datasheet register maps — microcontroller registers are described in hex addresses but manipulated with bitwise operations on binary values. Network engineers convert IP addresses between decimal and binary to understand subnetting and CIDR notation. Security professionals decode hex-encoded payloads and shellcode during malware analysis.

Powers of 2 — the key to base conversions

All base conversions to and from binary hinge on powers of 2. Memorising the first 16 powers is invaluable: 2^0=1, 2^1=2, 2^2=4, 2^3=8, 2^4=16, 2^5=32, 2^6=64, 2^7=128, 2^8=256, 2^9=512, 2^10=1024, 2^16=65536, 2^32=4,294,967,296. These numbers appear constantly in computing — memory sizes (256 MB, 1 KB = 1024 bytes), port numbers, colour channel values (0–255), and binary flags.

How to convert manually — step by step

To convert decimal to binary: repeatedly divide by 2 and record the remainders from bottom to top. For example, 42 ÷ 2 = 21 R0, 21 ÷ 2 = 10 R1, 10 ÷ 2 = 5 R0, 5 ÷ 2 = 2 R1, 2 ÷ 2 = 1 R0, 1 ÷ 2 = 0 R1 → reading remainders bottom-up: 101010. To convert binary to decimal: multiply each bit by its positional power of 2 and sum. For any other base pair, convert to decimal first, then to the target base.