Hex, Decimal, Octal & Binary Converter

Reference table

Converting by hand

Hex to decimal

Each hex digit is a power of 16, counting from the right. 2F is 2×16 + 15 = 47. 1A3 is 1×256 + 10×16 + 3 = 419. The letters A–F stand for 10–15.

Hex to binary

This one is mechanical, and it is why hex exists: each hex digit is exactly four binary digits. F is 1111, A is 1010, so FA is 1111 1010. No arithmetic required — just substitute. That four-bit group is a nibble, and it is why the binary field above is grouped in fours.

Decimal to binary

Halve repeatedly and record the remainders, then read them bottom to top. 13 → 6 r1, 3 r0, 1 r1, 0 r1 → 1101.

The bitwise operations

Masking is the everyday use: value & 0xFF keeps the low byte, value | 0x80 sets the top bit of a byte, and (rgb >> 16) & 0xFF pulls the red channel out of a packed colour.

Where this tool stops

Two real limits, both of which the app does not have. JavaScript's bitwise operators are 32-bit and signed, so ~12 shows as −13 and anything past 2³¹ wraps. And whole numbers above 2⁵³ cannot be represented exactly in a browser at all.

CalcBoard's programmer mode keeps all four bases on screen permanently rather than in a converter box, has hex A–F keys on the keypad, and falls back to arbitrary-size integers instead of overflowing. It is part of the one-time $2.99 Premium unlock.

Frequently Asked Questions

How do I convert hex to decimal?

Multiply each digit by its power of 16 and add. 2F is 2×16 + 15 = 47. A–F represent 10–15. The converter above does it as you type, in both directions.

Why is hexadecimal used in programming?

Because one hex digit maps exactly onto four binary digits, so hex is a compact, lossless shorthand for binary. FF is 1111 1111 — one byte in two characters — with no arithmetic needed to translate.

What is 0xFF in decimal?

255. It is the largest value that fits in one 8-bit byte, which is why it turns up constantly as a mask and as the maximum for a colour channel.

What does the AND operator do?

It compares two numbers bit by bit and returns 1 only where both bits are 1. 12 (1100) AND 10 (1010) = 8 (1000). It is most often used to mask out the bits you do not want.

Does this handle 64-bit values?

Not reliably — browser bitwise operations are 32-bit and signed. CalcBoard's programmer mode falls back to arbitrary-size integers, so large values stay exact.