Hex Calculator

One hex digit is four bits, and that is the whole reason

Sixteen is two to the fourth, so a single hex digit encodes exactly four bits — and two digits encode exactly one byte, the unit that matters everywhere in computing.

Memorise hex-to-binary in one direction only. The other direction is just reading the bits in groups of four, which is the reason hex exists: a 32-bit value is 8 hex digits instead of 32 characters, and a single typo in a byte is visible at a glance.

Why colour codes are hex

An RGB colour has three components, and each fits in one byte: red, green and blue from 0 to 255. Written as bytes that is six hex digits, and CSS reads them in that order.

#1D4ED8 is R = 0x1D = 29, G = 0x4E = 78, B = 0xD8 = 216, so rgb(29, 78, 216). Those are the exact values from this site's own palette. The shorthand #1D4 form is the same colour with each digit doubled — 0x1 → 0x11, 0xD → 0xDD — which is why #abc expands to #aabbcc and not to something else.

Adding a fourth byte gives alpha, so #1D4ED8FF is fully opaque and #1D4ED800 fully transparent. This 3-byte-plus-optional-alpha structure is why hex is the natural colour notation, and it is the same reason a memory dump is naturally grouped in pairs.

Masks, and why 0xFF is everywhere

A mask selects which bits you care about. Because a byte is two hex digits, 0xFF is the all-ones byte, and x & 0xFF keeps the low byte and discards everything above it. That single expression is the foundation of every binary protocol parser: it is how you read one byte out of a buffer.

• 0xFF — the low byte
• 0x0F — the low nibble, one hex digit
• 0x7F — clears the sign bit of a byte; the usual absolute value trick
• 0xFFFF / 0xFFFFFFFF — 16-bit and 32-bit all-ones

Where hex goes wrong

• Signed versus unsigned. 0xFF is 255 unsigned and −1 signed. The bits are identical; only the type declaration differs. This produces a class of bug where a length byte reads as 255 in one place and −1 in another.
• JavaScript's number limit. Numbers are doubles, exact to 2^53. A 16-hex-digit value is 64 bits and cannot be held exactly — parseInt('FFFFFFFFFFFFFFFF', 16) is not 18,446,744,073,709,551,615. Anything wider than 8 bytes needs BigInt or a string, not a number.
• Leading zeros matter. 0x7 is 00000011 in a byte but 111 in binary. When reading a binary protocol, pad to the byte width first or the positions shift.
• Confusing a number with a string. JavaScript's parseInt stops at the first invalid character and returns what it got, so parseInt('1D4ED8xyz', 16) succeeds with a partial value instead of failing.

Frequently asked questions

How do I convert hex to decimal?

Expand each digit to its 4-bit binary form and sum the powers of two, or divide by 16 repeatedly and read the remainders up. 0x1D4ED8 = 1×16^5 + 13×16^4 + 4×16^3 + 14×16^2 + 13×16 + 8 = 1,925,080.

What is the decimal value of 0xFF?

255 unsigned. In signed two's complement the same byte means -1, because inverting 00000001 and adding 1 produces 11111111. Which one applies depends on how the value is typed, not on the bits.

Frequently asked questions

1. How do I convert hex to decimal?

Expand each digit to its 4-bit binary form and sum the powers of two, or divide by 16 repeatedly and read the remainders up. 0x1D4ED8 = 1x16^5 + 13x16^4 + 4x16^3 + 14x16^2 + 13x16 + 8 = 1,925,080.

2. What is the decimal value of 0xFF?

255 unsigned. In signed two's complement the same byte means -1, because inverting 00000001 and adding 1 produces 11111111. Which one applies depends on how the value is typed, not on the bits.

3. Why do colour codes use six hex digits?

An RGB colour has three components of one byte each, so 3 x 2 = 6 hex digits in red-green-blue order. The 3-digit shorthand #abc doubles each digit to #aabbcc.

4. Why does JavaScript give the wrong answer for large hex numbers?

JavaScript numbers are doubles, exact only to 2^53. A 16-hex-digit value is 64 bits and exceeds that, so parseInt returns an approximation. Use BigInt or keep such values as strings.