CalKit

Base Converter

Convert between number bases.

변환 결과 (2진법 (Binary))
11111111

10진법 (Decimal): 255 → 2진법 (Binary): 11111111

모든 진법 표현

2진법 (Binary)11111111
8진법 (Octal)377
10진법 (Decimal)255
16진법 (Hex)FF

Overview

The Base Converter converts between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). It is essential for computer science, programming, and digital systems study.

Formula

Decimal → Binary: Repeatedly divide by 2 and read remainders in reverse.
Example: 13₁₀ = 1101₂

Binary → Decimal: Sum of each digit × 2^(position)
Example: 1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13₁₀

Hexadecimal: 0-9, A=10, B=11, C=12, D=13, E=14, F=15
Example: FF₁₆ = 255₁₀

How to Use

  1. 1Enter the number to convert.
  2. 2Select the base of the input number (2, 8, 10, or 16).
  3. 3Conversion results to all bases are displayed simultaneously.

Tips

  • ✔One hex digit corresponds to four binary digits (e.g., F₁₆ = 1111₂).
  • ✔One octal digit corresponds to three binary digits (e.g., 7₈ = 111₂).
  • ✔In programming, hex is used for color codes (#FF0000), memory addresses, and more.

FAQ

Q. Why do computers use binary?

The basic unit of a computer, the transistor, distinguishes only two states: on (1) and off (0). All data — text, images, music — is ultimately stored as combinations of 0s and 1s.

Q. Why is hexadecimal used?

Binary numbers can be very long and hard to read. Hexadecimal compresses every 4 binary digits into a single digit, making computer-related values like memory addresses and color codes much more concise.

Q. How do you handle decimal points in base conversion?

Separate the integer and fractional parts. The integer part uses repeated division; the fractional part uses repeated multiplication. Example: 0.625₁₀ → 0.625×2=1.25, 0.25×2=0.5, 0.5×2=1.0 → 0.101₂.

Related Calculators

Percentage Calculator

Calculate percentages, discounts, and rate of change.

Ratio Calculator

Simplify ratios and solve proportions.

Quadratic Equation Solver

Solve quadratic equations in the form ax² + bx + c = 0.

Fraction Calculator

Calculate fraction arithmetic and simplification.

GCD/LCM Calculator

Calculate greatest common divisor and least common multiple.

Standard Deviation Calculator

Calculate mean, variance, and standard deviation of data.