Binary

Computer Science & Digital Logic Number Systems

Computers operate on base-2, base-8, base-10, and base-

16.

Primary Positional Radix Formulas

• Binary to Decimal: D = Σ_i=0^n-1 b_i × 2^i

• Hexadecimal Mapping: Each hex digit represents exactly 4 binary bits.

• Octal Mapping: Each octal digit represents exactly 3 binary bits.

• 8-Bit Byte Structure: Bit 0 to Bit

7.

How to Use This Calculator

Enter your Number to Convert (e.g. 42) and Input Number Base — choose from Decimal (Base 10), Binary (Base 2), Hexadecimal (Base 16). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Binary

Input variables:

inputNumberString — Number to Convert

inputBaseSelect — Input Number Base

Computed outputs:

binaryRepresentation — Binary (Base 2)

decimalRepresentation — Decimal (Base 10)

hexRepresentation — Hexadecimal (Base 16)

octalRepresentation — Octal (Base 8)

binaryPadded8Bit — 8-Bit Formatted Byte

Standard: NIST Handbook 44 and BIPM SI unit definitions

Worked Example

The number 42 is represented in computer RAM as the binary byte 00101010, which translates to hex 0x2A.

Understanding Your Result

Unit conversions are exact by definition within a given measurement system (e.g., 1 km = exactly 1,000 m). Cross-system conversions (metric to imperial) use defined exchange factors: 1 inch = exactly 2.54 cm; 1 pound = 0.45359237 kg. Round your converted result to match the precision of your original measurement — expressing more decimal places than your input justifies implies false accuracy. For regulatory, legal, or safety-critical applications, verify which measurement system is required by the applicable standard.