Binary / Hex / Decimal Converter

Programmers, students and electronics hobbyists constantly move numbers between bases: a colour in hex, a register in binary, a permission mask in octal, a value in decimal. FreePDF’s converter shows all of them side by side the moment you type, handles numbers of any size without precision loss, and adds the views that are usually missing from simple converters – two’s-complement for signed integers, byte counts and the Unicode character a code point represents. All maths happens locally in your browser.

Common uses

• Translate hex values from a debugger or memory dump into decimal.
• Check binary bit masks and flags while writing embedded or networking code.
• Work through computer-science homework on number systems and signed integers.
• Convert Unix permissions such as 755 between octal and binary.
• Find the Unicode code point of a character, or the character for a code point.

Tips for best results

• Binary output is grouped in fours (nibbles) and hex in pairs (bytes) to make long values readable.
• Choose 8, 16, 32 or 64-bit width to see how a negative number is stored in two’s complement.
• Type a negative number (e.g. -42) with any base – the sign is kept separately from the digits.
• Base 36 uses 0–9 and a–z, handy for short IDs and URL shorteners.
• Download the result as text to paste into notes or documentation.

Why computers use binary and hex

Digital circuits have two stable states, so computers store everything as binary digits (bits). Long strings of ones and zeros are hard for humans, so we group them: three bits make one octal digit, four bits make one hexadecimal digit. That is why a byte (8 bits) is always exactly two hex digits, from 00 to FF, and why colours, MAC addresses and memory addresses are written in hex. Decimal remains the base people think in, which is why converting quickly between them matters.

Signed numbers and two’s complement

Computers store negative integers using two’s complement: invert all bits of the positive value and add one. In 8 bits, −1 becomes 11111111 (0xFF) and −128 becomes 10000000. The same bit pattern can therefore mean 255 or −1 depending on whether the type is unsigned or signed. When you choose a bit width the converter shows the stored pattern, its hex form, and how it reads as signed and unsigned, and warns you when a value does not fit in that width.

Converting by hand

To convert decimal to another base, divide repeatedly by the base and read the remainders from bottom to top: 13 ÷ 2 gives remainders 1, 0, 1, 1, so 13 = 1101 in binary. To go back, multiply each digit by the base raised to its position and add: 1×8 + 1×4 + 0×2 + 1×1 = 13. Hex works the same way with base 16, using A–F for 10–15. The tool does this instantly, but knowing the method helps you sanity-check results in exams and interviews.