Hex to Binary Converter

No arithmetic is involved. Sixteen is two to the fourth, so each hex digit stands for exactly one pattern of four bits and the patterns never interact. You can translate a value of any length one character at a time, in any order, and still get the right answer.

1. Take the hex digits one at a time, left to right.
2. Look up each digit’s four-bit group in the nibble table.
3. Write the groups side by side in the same order, keeping every inner zero.
4. Optionally drop the zeros at the very front, unless you need a fixed width.

The one rule to respect is padding inside the number. The digit 3 is 0011, not 11: if you shorten an inner group, every bit to its left slides into the wrong place and the value changes.

The nibble table

A nibble is half a byte. These sixteen rows are the whole lookup; learn a few anchors and the rest follow. 8 is a lone high bit (1000), F is all four set, and A and 5 are the alternating patterns 1010 and 0101 that test engineers like because neighboring bits differ.

A digit and its complement to F are bit-for-bit opposites: 3 and C, 6 and 9, 1 and E. That pairing is handy when you are checking a mask and its inverse.

Reading flag bytes

Status registers and option fields pack several yes-or-no switches into one byte, and documentation lists them as hex masks. Expanding the byte to bits shows which switches are on. The 6502 processor status register, laid out in MOS Technology’s MCS6500 programming manual, is a classic: a value of C3 is 1100 0011, so Negative, Overflow, Zero and Carry are set.

Each mask has a single 1 in it, so it is always 1, 2, 4 or 8 in one of the two digit positions. Testing a flag in code is status & 0x40, and the hex calculator can show that AND bit by bit.

Mathematically, 0011 1100 1001 and 1111001001 are the same number. Which one to write depends on what the bits mean. A register, a byte in a packet or a pixel channel has a fixed size, and the high zeros are real bits that happen to be off; dropping them hides the size. A plain quantity has no width, and the short form is cleaner.

The converter always groups binary in nibbles and keeps the zeros needed to complete the leftmost group only when a bit width is chosen on the home converter. Here the result keeps its natural length.