About

Number systems are the foundation of digital logic. While humans operate in Base-10 (Decimal), hardware operates in Base-2 (Binary). Programmers frequently use Base-16 (Hexadecimal) as a concise shorthand for binary data. This converter transforms integer values across these four primary systems.

Understanding positional notation is critical for network subnetting, color coding (RGB), and memory addressing. An error in base conversion can lead to buffer overflows or incorrect addressing logic in low-level programming.

Formulas

To convert from any base b to decimal, we sum the products of digits d and their positional weights:

Value = n∑i=0 d_i ⋅ bⁱ

To convert from decimal to binary, we use repeated division by 2 and record the remainders.

Reference Data

Decimal (10)	Binary (2)	Octal (8)	Hexadecimal (16)
0	0000	0	0
1	0001	1	1
10	1010	12	A
15	1111	17	F
16	10000	20	10
255	11111111	377	FF

Frequently Asked Questions

This tool uses standard Javascript integer safety limits (2^53 - 1). For extremely large numbers used in cryptography, specialized BigInt calculators are required.

Base-16 requires 16 unique symbols. We use 0-9 for the first ten, and A, B, C, D, E, F to represent values 10 through 15. This convention prevents confusion that would arise from using double digits like "10" or "11" as single symbols.

Octal (Base-8) was common in early computing (like the PDP-8) and is still used in Unix file permissions (e.g., chmod 755). Each Octal digit maps perfectly to 3 bits of binary.