How do I convert binary to decimal?

Multiply each binary bit by its power of 2 and add the results. For example, 1010 equals 8 plus 2, so it is decimal 10.

How do I convert decimal to binary?

Repeatedly divide the decimal number by 2 and read the remainders in reverse order, or use this converter to generate the binary value directly.

What is hexadecimal used for in digital electronics?

Hexadecimal is a compact way to write binary data because each hex digit represents exactly four binary bits.

Number System Converter | Binary Decimal Hex Octal

Number System Converter

Convert binary, decimal, hexadecimal and octal numbers for digital logic, microcontrollers, registers, memory addresses and programming.

🔢 Digital Rule: Hex is compact binary. Each hex digit equals exactly 4 bits, and each octal digit equals exactly 3 bits. Use this with the Binary Converter, Two’s Complement Calculator, Gray Code Converter and Truth Table Generator.

🔢 Number Systems Used in Digital Logic

Input Number

Input Base

Bit Grouping

Prefix Format

Accepts prefixes such as 0b1010, 0x2A and 0o52. Spaces and underscores are ignored.

Examples:

Decimal Value

Bit Width

Display Format

Input Type

Signed Binary Optional

Use this when you need fixed-width binary for registers, ADC values, signed integers or two’s complement representation.

Presets:

Input Value

From Base

To Base

Uppercase Output

For arbitrary base conversion, digits can use 0–9 and A–Z. Base must be between 2 and 36.

Examples:

Base

Operation

Bitwise AND / OR / XOR are useful for masks, registers and digital logic states.

Examples:

📐 Formula Reference

Binary to Decimal

decimal = Σ(bit × 2^position)

Hex to Binary

1 hex digit = 4 binary bits

Octal to Binary

1 octal digit = 3 binary bits

Signed Range

n-bit signed range = -2^(n-1) to 2^(n-1)-1

📋 Quick Reference

Common Values

1111₂15 / F₁₆

11111111₂255 / FF₁₆

10000000₂128 / 80₁₆

Bit Width

4 bits1 hex digit

8 bits2 hex digits

16 bits4 hex digits

Prefixes

Binary0b

Octal0o

Hex0x

📚 Digital Logic Notes

Why hex is popularHexadecimal is easier to read than long binary strings. An 8-bit byte such as 11111111 becomes FF.

Unsigned vs signedThe same binary pattern can mean different values. 11111111 is 255 unsigned, but -1 in 8-bit two’s complement.

Bit width mattersFixed-width systems like 8-bit, 16-bit or 32-bit registers can overflow, wrap or change sign depending on interpretation.

Use with logic toolsAfter converting values, use the Truth Table Generator or Boolean Algebra Calculator to analyze logic behavior.

What is a Number System Converter?

A number system converter changes a value between binary, decimal, octal and hexadecimal. These number systems are used in digital electronics, microcontrollers, memory addresses, registers, programming and Boolean logic.

Why convert binary to hex?

Hexadecimal is a compact representation of binary. Four binary bits make one hex digit, so long binary values become easier to read, copy and debug.

Binary, decimal, hex and octal difference

Binary uses base 2, decimal uses base 10, octal uses base 8 and hexadecimal uses base 16. The value can be the same, but the written representation changes.

❓ Frequently Asked Questions

Multiply each bit by a power of 2 based on its position and add the results. Example: 1010₂ = 8 + 2 = 10₁₀.

Divide the decimal number by 2 repeatedly and read the remainders from bottom to top. The calculator does this instantly and can also pad the result to a selected bit width.

Replace each hexadecimal digit with its 4-bit binary equivalent. For example, A₁₆ = 1010₂ and F₁₆ = 1111₂.

255 in unsigned decimal is 11111111 in binary and FF in hexadecimal.

Unsigned binary uses all bits for magnitude. Signed two’s complement uses the most significant bit as the sign indicator, so the same bit pattern can represent a negative value.

Hex is compact and maps directly to binary groups of four bits, making it convenient for memory addresses, register values, color codes, machine code and debugging.