Convert a whole number from binary (base 2) to hexadecimal (base 16) using exact four-bit groups.
Enter a binary integer using only 0 and 1.
Up to 1,000 binary digits are accepted. Output uses uppercase A–F and omits unnecessary leading zeroes.
Binary and hexadecimal are two ways of writing the same integer. Binary uses digits 0 and 1; hexadecimal uses 0–9 and A–F. This calculator rewrites a binary integer in hexadecimal and displays letters in uppercase.
Each hexadecimal digit corresponds exactly to four binary bits, so the conversion can be checked by grouping from the right. The calculator maps bit groups directly and preserves up to 1,000 input bits exactly.
Enter the binary digits in the Binary Number field, then choose Convert to hexadecimal. Use only 0 and 1 for a nonnegative integer. Do not include a 0b prefix, spaces, punctuation or a decimal point. Up to 1,000 bits are accepted.
For a manual check, group bits in fours from the right, padding only the leftmost group with zeroes. Map 0000 through 1111 to hexadecimal digits 0 through F. The output uses uppercase letters; lowercase represents the same values.
| Input | Meaning |
|---|---|
| Binary number | A nonnegative integer represented using bits 0 and 1, with no spaces or prefixes. |
| Hexadecimal output | The same integer in base 16, using 0–9 and A–F. |
| Input length | Up to 1,000 bits; conversion is exact. |
The rightmost bit contributes 1, the next 2, then 4, 8, 16 and successive powers of two. A zero bit contributes nothing at that position but still determines the positions of bits to its left.
Hexadecimal place values are 1, 16, 256, 4096 and successive powers of sixteen. For example, 2A represents 2×16 + 10 = 42 in decimal.
Leading zeroes do not change the integer value, though they can indicate a fixed bit width. The calculator returns a minimal hexadecimal representation; preserve the intended width separately if it matters.
For 101010₂, group from the right as 10|1010. Pad the left group for checking: 0010|1010. The groups are 2 and A, so the hexadecimal result is 2A. In decimal, 32+8+2=42, matching 2×16+10.
For 11111111₂, group 1111|1111. Each group is fifteen, written F, so the result is FF. Its decimal value is 15×16+15=255.
For 100000000₂, group 1|0000|0000, yielding 100₁₆. The value is 256, not one hundred.
Use hexadecimal to inspect bit patterns more compactly. Keeping groups aligned makes it easier to compare bytes or identify changed positions. A change in one hex digit corresponds to a change within its four-bit group, rather than a change in an unrelated decimal grouping.
The calculator does not assign a signed interpretation. A bit pattern such as 11111111 can represent the unsigned integer 255, or a different value under a signed encoding such as eight-bit two’s complement. This page’s ordinary base conversion gives the unsigned positional value rather than deciding the encoding for you.
Byte order is another separate matter. A whole integer’s base conversion does not establish how bytes are arranged in a file or memory representation. If a protocol uses little-endian order, that convention must be handled separately from the digit conversion.
Do not enter decimal 42 to ask for its binary-to-hex conversion; 4 and 2 are not binary digits. Group from the right and pad only the leftmost group. Do not discard internal zeroes or pad on the right, because either can change the represented value.
The form accepts only 0 and 1 and rejects strings longer than 1,000 bits. Direct four-bit grouping keeps the conversion exact without floating-point base conversion.
They do not change the integer value. They can still carry width information, such as a sixteen-bit field. The conversion does not preserve that metadata, so pad the result separately if a specification requires fixed width.
The binary group 1010 has value 8+2=10. Hexadecimal uses A for ten so each digit remains a single symbol. B through F represent eleven through fifteen.
No. This page accepts whole-number bit strings only. A binary fraction such as 0.101 needs a separate fractional-place conversion.
No. As an unsigned hexadecimal integer, FF is 255. It represents −1 only under a specified signed encoding and width, such as eight-bit two’s complement. This calculator performs unsigned positional conversion.
Yes, within the 1,000-bit input limit. The converter groups bits directly in fours and does not pass through floating-point arithmetic.