Binary, Hex & Octal Converter

Frequently Asked Questions

What are binary, octal, decimal, and hexadecimal?

They are number systems using base 2, 8, 10, and 16 respectively. Decimal uses 0-9, hexadecimal uses 0-9 and A-F where A = 10 and F = 15.

Why does computing use binary and hexadecimal?

Computers store data as on/off bits (binary). Hex is a compact way to display binary because each hex digit equals exactly 4 bits, making memory addresses readable.

How do I convert decimal to binary by hand?

Repeatedly divide by 2 and record the remainders. Read the remainders bottom-up. So 13 gives 6 r1, 3 r0, 1 r1, 0 r1 which reads as 1101.

What is the largest number an 8-bit value can hold?

Unsigned 8-bit holds 0 to 255 (2⁸ - 1). Signed 8-bit holds -128 to 127 using two's complement.

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How This Calculator Works

Select the base of your input number, type the value, and the converter immediately displays the equivalent in all four common numeral systems: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Internally the input is parsed into a decimal integer, which then serves as the intermediate value for every output base, so the same engine handles any direction of conversion accurately.

Formula

Positional notation gives each digit a weight equal to the base raised to its position. To read a number in any base back to decimal:

value = Σ digit_i × baseⁱ

For example, decimal 345 = 3 × 10² + 4 × 10¹ + 5 × 10°. To go from decimal to another base, repeatedly divide by the target base and read the remainders in reverse order.

Common Mistakes

Including a prefix (0x, 0b, 0o) inside the digits when the base is already selected.

Using digits that are invalid for the chosen base - for example a 9 in octal, which only allows 0-7.

Forgetting that hex uses letters A-F for the values 10-15.

Reading division remainders top-to-bottom instead of bottom-to-top.

Confusing nominal digit count with bit count - one hex digit equals four binary bits, not one.

Tips & FAQ

Q: Why is hex everywhere in programming? A byte is 8 bits; two hex digits represent exactly one byte, so memory addresses (0x1A3F) and colors (#4A90E2) are far easier to read than 8-digit binary.

Q: Why does binary matter? Transistors have two states, on (1) and off (0), so all computer storage is fundamentally base 2.

Q: What is octal used for? Historically in Unix file permissions and as binary shorthand - each octal digit maps to exactly three binary bits.

Q: Can I convert fractions? This tool converts integers; fractional base conversion uses a separate multiply-by-base technique on the fractional part.

Binary, Hex & Octal Converter

Frequently Asked Questions

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