Hex to binary converter
Enter a hex number and get its binary value instantly, plus the other bases and the step-by-step working. Handles huge numbers, negatives and fractions.
Working for 7E316
Each hex digit is exactly 4 bits, so you can convert group by group, no arithmetic needed:
How to convert hex to binary
- Replace each hex digit with its 4-bit pattern: 0 = 0000, 7 = 0111, A = 1010, F = 1111.
- Keep leading zeros inside the number; you can drop them at the very front.
- 3C = 0011 1100 = 111100.
Hex is the shorthand for bytes: colour codes (#FF8800), memory addresses, MAC addresses, Unicode code points and hash digests are all written in it. Binary is how hardware stores everything: bit flags, network masks, file permissions and machine code are all patterns of 1s and 0s.
See place value move
Every bit is worth twice the bit to its right. Flip the switches and watch the decimal, hex and octal values rebuild.
32 + 8 + 4 + 1 = 45 · hex 2D · octal 55
Related conversions
Binary to hex · Octal to binary · Decimal to binary · Hex to octal · Hex to decimal · any base 2–36 · signed (two's complement)
Questions people ask
How do you convert hex to binary?
Replace each hex digit with its 4-bit pattern: 0 = 0000, 7 = 0111, A = 1010, F = 1111. Keep leading zeros inside the number; you can drop them at the very front. 3C = 0011 1100 = 111100.
What is 7E3 in binary?
7E3 in hex (base 16) is 11111100011 in binary (base 2).
Does it handle negative numbers and fractions?
Yes. A leading minus sign is kept, and digits after a point are converted too. Some fractions that end in one base repeat forever in another (0.1 in decimal is 0.000110011… in binary), so the result is cut at 24 digits and marked as repeating.
Is there a size limit?
No practical one. The converter uses arbitrary-precision integers (JavaScript BigInt), so 64-bit, 128-bit and longer values convert exactly, without rounding.
Why is there no arithmetic in the working?
Every hex digit maps to a fixed group of bits, so conversion is a lookup rather than a calculation.