Introduction / overview

Decimal to Hexadecimal Converter turns any whole decimal number into its hexadecimal equivalent — and, because every four binary digits collapse into a single hex digit, it also shows the binary value grouped into nibbles so $0000000000001100$ reads as $0000\ 0000\ 0000\ 1100$ instead of a wall of digits.

Negative values are handled with two’s complement, and the conversion is an exact integer operation — nothing is rounded. By default the tool works in a 16-bit representation, and you can switch to any width from 2 to 20 bits.

It is the tool to reach for when you are reading a hex value from code, an address, a color, a register dump, or a network trace, and you need to know what decimal value sits behind it. Programmers, students, and anyone learning how computers store integers all end up converting decimal to hex sooner or later.

How to use / quick start

1

Enter a whole decimal number

Type the value into the Decimal field. The input domain shown above the field (for example −32,768 to 32,767 at the default 16 bits) tells you what fits in the current representation. Whole numbers only — decimals and fractions are not converted.

2

Read the Binary and Hexadecimal results

The Binary row shows the value padded to the selected bit width and grouped in blocks of four; the Hexadecimal row shows the uppercase hex form you can copy straight into code or documentation.

3

Change the bit width when you need to

Turn on Change the binary representation to pick a preset — 4, 8, 12, or 16 bits — or choose Other and type any width from 2 to 20. A wider representation accepts a wider range of values.

Example — convert 4987 to hex

Type $4987$ in the Decimal field. Repeating the “divide by 16, keep the remainder” step from the bottom up:

4987 \div 16 = 311\ \text{r}\ 11

311 \div 16 = 19\ \text{r}\ 7

19 \div 16 = 1\ \text{r}\ 3

1 \div 16 = 0\ \text{r}\ 1

Reading the remainders from last to first gives $137B_{16}$ . The tool shows Binary: 0001 0011 0111 1011 and Hexadecimal: 137B at the default 16-bit width.

Calculation method

For a non-negative value, the binary representation is just the usual place-value encoding padded with leading zeros to the chosen width. For a negative value, the tool uses two’s complement: it adds $2^n$ to the number, then encodes that result in $n$ bits.

B = N,\ \text{for } N \ge 0

\qquad B = N + 2^n,\ \text{for } N < 0

The hexadecimal result is produced from the same encoded value: starting from the right, the bits are split into groups of four (nibbles), and each group maps to a single hex digit.

H = \sum_{k=0}^{m-1} h_k \cdot 16^{k},\qquad h_k = 8 b_{4k+3} + 4 b_{4k+2} + 2 b_{4k+1} + b_{4k}

Worked example — negative value

For $-87$ at 16 bits, the encoded value is $-87 + 2^{16} = 65449$ , which is $1111\ 1111\ 1010\ 1001$ in binary:

-87

\ \to\

1111\ 1111\ 1010\ 1001_2

\ \to\

\mathrm{FFA9}_{16}

Every negative value therefore starts with a run of $1$ bits — that leading $\mathrm{F}$ nibble is the two’s-complement “sign marker”, not a large number.

Variables

$N$ — the decimal input value
$B$ — the encoded value held in $n$ bits
$n$ — the bit width (2–20)
$h_k$ — the $k$ -th hex digit (0–9, A–F)
$b_i$ — the bit at position $i$ (0 or 1)

Conversion is one-directional: the Binary and Hexadecimal rows are read-only results derived from the Decimal input. If you already have a hexadecimal value and want its decimal form, use the binary to hexadecimal converter, which converts both ways.

Bit width and why hex is used

Each bit width has a signed range

An $n$ -bit two’s-complement value covers $[-2^{n-1},\ 2^{n-1} - 1]$ . That is why the input domain note changes with the representation: 8 bits allow −128 to 127, 16 bits allow −32,768 to 32,767, and 20 bits allow −524,288 to 524,287. If your number is outside the current range, switch to a wider representation instead of leaving it blank.

Four bits are one hex digit

A nibble holds a value from $0$ to $15$ — exactly one hex digit. So an 8-bit byte always reads as two hex digits, and a 16-bit value always reads as four, which is why colors, memory addresses, and hash outputs are written in hex.

Signed versus unsigned

The same bit pattern can mean different numbers. In an 8-bit unsigned interpretation $\mathrm{FF}$ is $255$ ; in the signed two’s-complement reading this tool uses, it is $-1$ . The result here always reflects the signed interpretation for the selected width.

If you want to focus on the binary form, the binary converter shows decimal-to-binary and binary-to-decimal with the same fixed-width, two’s-complement handling. For octal, base64, or any base between 2 and 64, the integer base converter is a more general tool.

Frequently asked questions

Why is −1 shown as FFFF at 16 bits?

Because two’s complement encodes $-1$ as $-1 + 2^{16} = 65535$ , which is $1111\ 1111\ 1111\ 1111$ in binary — and $\mathrm{FFFF}$ in hex. The leading run of $1$ s is the sign marker; the same pattern would mean $65535$ only if interpreted as unsigned.

Why do I see “Your data input exceeds the allowed limits”?

The number is too large (or too negative) for the current bit width. For example, at 8 bits the largest value is $127$ , so $300$ is rejected. Turn on Change the binary representation and pick a wider width — the input domain note updates immediately to show the new range.

Why does the binary result start with so many zeros?

The value is padded to fill the selected bit width, then grouped into nibbles. At 16 bits, $12$ becomes $0000\ 0000\ 0000\ 1100$ . The leading zeros are part of the fixed-width representation and do not change the value.

Can I convert hexadecimal back to decimal here?

Not on this page — the output is read-only and the conversion is one-directional. To go the other way, or to convert between binary and hexadecimal directly, use the binary to hexadecimal converter.

Limitations

This calculator accepts whole decimal numbers only — a decimal point or fraction produces an “Enter a whole number.” message and nothing is converted. The bit width is limited to 2–20 bits, with 16 bits as the default. Negative values are interpreted as signed two’s complement, so the same input produces different binary and hex output at different widths, and numbers outside the current width’s range are not converted until you widen the representation. There is no hex-to-decimal direction on this page.

Decimal to Hexadecimal Converter

Introduction / overview

How to use / quick start

Calculation method

Frequently asked questions

Why is −1 shown as FFFF at 16 bits?

Why do I see “Your data input exceeds the allowed limits”?

Why does the binary result start with so many zeros?

Can I convert hexadecimal back to decimal here?

Limitations

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