How do you convert binary to hex?
Split the bits into groups of four from the right and replace each group with one hex digit. 1101 0110 becomes D6, so the number is 0xD6.
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Hex converter (binary, decimal, octal)
Type a number into this hex converter and read it in binary, decimal and octal at 8, 16, 32 or 64 bits, signed or unsigned. Any field takes input, so it works just as well as a binary to hex converter. You can also flip individual bits and read the byte order and the C literal for the same value.
Bit width
Read as
Bits (click a bit to flip it, most significant first)
B1C0
B0DE
16-bit unsigned value
49,374
0xC0DE
- Unsigned
- 49,374
- Signed (two’s complement)
- -16,162
- Bits set
- 8 of 16
- Range of this type
- 0 to 65,535
C literal
uint16_t value = 0xC0DEu;Byte order in memory
| Address offset | +0 | +1 |
|---|---|---|
| Big-endian | C0 | DE |
| Little-endian | DE | C0 |
How do you convert binary to hex?
Group the bits in fours from the right and replace each group with one hex digit, because 16 = 2⁴. For example 1101 0110 is 0xD6, which is 214 as an unsigned number and -42 as an 8-bit signed (two’s complement) number.
How a base converter works
Each base is the same positional sum with a different radix, so a hexadecimal to decimal converter and a binary to decimal converter run the same arithmetic. Hex and binary line up because one hex digit is exactly four bits; octal digits are three bits, so they do not line up with bytes.
value = Σ d_i × r^i
- d_i
- the digit at position i, counted from 0 at the right
- r
- the base: 2, 8, 10 or 16
A signed N-bit value uses the same bits, with the top bit counted as negative:
value = −b_(N−1) × 2^(N−1) + Σ b_i × 2^i (i from 0 to N−2)
- b_i
- bit i, 0 or 1
- N
- the bit width
That is the same as subtracting 2^N whenever the top bit is set. Negation follows directly:
−x = (NOT x) + 1 signed value = pattern − 2^N, if the top bit is 1
Worked examples
Example 1: 1101 0110 in every base
The groups are 1101 = D and 0110 = 6, so the hex value is 0xD6. As an unsigned number it is 128 + 64 + 16 + 4 + 2 = 214. The top bit is set, so as an 8-bit signed number it is 214 − 256 = -42. In octal it is 326.
Example 2: −1000 as a 16-bit value
+1000 is 0000 0011 1110 1000 (0x03E8). Inverting every bit gives 1111 1100 0001 0111 (0xFC17), and adding one gives 0xFC18. The check: 65536 − 1000 = 64536, which is the unsigned reading of the same bits.
Example 3: 0xDEADBEEF in memory
Read as unsigned it is 3,735,928,559; read as a 32-bit signed number it is -559,038,737. A big-endian machine stores DE AD BE EF from the lowest address up, and a little-endian machine stores EF BE AD DE, which is what a hex dump of memory on an x86 or a typical Arm Cortex-M part shows.
Hex to binary and decimal table
One hex digit is one nibble. Memorize these and most conversions become reading.
| Hex | Binary | Decimal |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 2 | 0010 | 2 |
| 3 | 0011 | 3 |
| 4 | 0100 | 4 |
| 5 | 0101 | 5 |
| 6 | 0110 | 6 |
| 7 | 0111 | 7 |
| 8 | 1000 | 8 |
| 9 | 1001 | 9 |
| A | 1010 | 10 |
| B | 1011 | 11 |
| C | 1100 | 12 |
| D | 1101 | 13 |
| E | 1110 | 14 |
| F | 1111 | 15 |
Integer ranges by bit width
Limits of the exact-width C types, which are the same limits as any two’s complement register of that size.
| Bits | Signed minimum | Signed maximum | Unsigned maximum | Unsigned maximum (hex) |
|---|---|---|---|---|
| 8 | -128 | 127 | 255 | 0xFF |
| 16 | -32,768 | 32,767 | 65,535 | 0xFFFF |
| 32 | -2,147,483,648 | 2,147,483,647 | 4,294,967,295 | 0xFFFFFFFF |
| 64 | -9,223,372,036,854,775,808 | 9,223,372,036,854,775,807 | 18,446,744,073,709,551,615 | 0xFFFFFFFFFFFFFFFF |
8-bit two’s complement values
The same pattern reads differently depending on the type you store it in. Set the tool to signed and it works as a two’s complement calculator at 8, 16, 32 or 64 bits.
| Hex | Binary | Unsigned | Signed |
|---|---|---|---|
| 0x00 | 0000 0000 | 0 | 0 |
| 0x01 | 0000 0001 | 1 | 1 |
| 0x7F | 0111 1111 | 127 | 127 |
| 0x80 | 1000 0000 | 128 | -128 |
| 0x81 | 1000 0001 | 129 | -127 |
| 0xFE | 1111 1110 | 254 | -2 |
| 0xFF | 1111 1111 | 255 | -1 |
Where this goes wrong in real firmware
- Integer promotion: uint8_t and uint16_t operands are promoted to int before arithmetic, so ~x on a uint8_t holding 0xF0 is 0xFFFFFF0F on a 32-bit int, not 0x0F. Cast or mask the result back to the width you meant.
- Shifts on signed values: C11 6.5.7 gives no valid result for left-shifting a negative value or shifting into overflow, and leaves right-shifting a negative value up to the compiler. Do bit manipulation on unsigned types.
- Narrowing to a signed type: converting a value that does not fit is implementation-defined (C11 6.3.1.3), even though nearly every compiler simply keeps the low bits.
- Reading registers narrower than the variable: a 12-bit two’s complement sensor value in a 16-bit register needs sign extension. Subtract 4096 when bit 11 is set.
- Casting a byte buffer to a wider pointer: the result depends on endianness and may be a misaligned access. Assemble values from bytes with shifts instead.
The calculator covers the standard widths of 8, 16, 32 and 64 bits. It treats integers only, so floating-point and fractional formats need a separate conversion.
Glossary
- Bit width
- How many bits a value occupies. It sets the range and the position of the sign bit.
- Two’s complement
- A signed integer encoding in which the top bit has weight −2^(N−1).
- Sign extension
- Copying the sign bit into the new upper bits when widening a signed value, which keeps the value the same.
- Nibble
- Four bits, exactly one hex digit.
- Endianness
- The order in which the bytes of a multi-byte value are stored or sent.
- MSB and LSB
- The most significant and least significant bit (or byte) of a value.
Frequently asked questions
How do you convert hex to decimal?
Multiply each digit by its power of 16 and add. 0x2A is 2 × 16 + 10 = 42. Every field above updates as you type, so it works as a hex to decimal converter and a decimal to hex converter with no mode to switch.
How do you convert binary to decimal?
Add the power of two for every 1 bit. 1101 0110 is 128 + 64 + 16 + 4 + 2 = 214 as an unsigned number.
What is two’s complement?
The way nearly all hardware stores signed integers. The top bit counts as −2^(N−1) instead of +2^(N−1), so at 8 bits 0xFF is −128 + 127 = -1. To negate a number, invert every bit and add one.
What is the range of int8_t, int16_t, int32_t and int64_t?
An N-bit signed integer holds −2^(N−1) to 2^(N−1) − 1: -128 to 127, -32,768 to 32,767, -2,147,483,648 to 2,147,483,647, and -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807.
What is the difference between big-endian and little-endian?
The order of the bytes in memory. 0x12345678 is stored as 12 34 56 78 on a big-endian system and 78 56 34 12 on a little-endian one, starting from the lowest address. The value is the same; only code that reads memory byte by byte can tell.
Why can’t I write -2147483648 directly in C?
The minus sign is an operator applied to the constant 2147483648, which does not fit in a 32-bit int, so the constant takes a wider type. stdint.h avoids this by writing (-2147483647 - 1). For INT64_MIN it is a real problem, because 9223372036854775808 fits no standard signed type.
Can I write binary literals in C?
The 0b prefix is part of C23 (WG14 proposal N2549). Before that it is a compiler extension, available in GCC and Clang, so hex is the portable choice in older code bases.
Why do other converters get large 64-bit values wrong?
JavaScript numbers and spreadsheet cells are 64-bit floats, exact only up to 2^53 − 1. This page uses arbitrary-precision integers, so 9,007,199,254,740,993 correctly converts to 0x0020000000000001.
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Sources
- ISO/IEC 9899:2011 (C11) committee draft N1570: integer constants (6.4.4.1) and exact-width types and limits (7.20)
- WG14 N2412, Two’s complement sign representation for C2x
- WG14 N2549, Allow for binary integer constants
- Danny Cohen, IEN 137, On Holy Wars and a Plea for Peace (the origin of big-endian and little-endian)
- RFC 1700, Assigned Numbers: Data Notations (big-endian order in Internet protocols)
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