Convert Number Display Format

Convert hexadecimal, decimal, octal, and binary numbers between different formats

Number Format Converter

Number System Conversion

With this function, an integer is converted and displayed in different formats. The number can be entered in hexadecimal, decimal, octal or binary format.

Hex: 0-9, A-F | Dec: 0-9 | Oct: 0-7 | Bin: 0-1
Results
Binary:
Octal:
Decimal:
Hexadecimal:

Number Systems Overview

Binary

Base 2

Digits: 0, 1

Digital Foundation
Octal

Base 8

Digits: 0-7

Unix Permissions
Decimal

Base 10

Digits: 0-9

Standard System
Hexadecimal

Base 16

Digits: 0-9, A-F

Programming
Important Properties
  • The result is displayed in all four formats
  • Hexadecimal: A=10, B=11, C=12, D=13, E=14, F=15
  • Binary system: Foundation of all computer technology
  • Octal system: Compact representation of 3-bit groups

Mathematical Foundations of Number System Conversion

The conversion between different number systems is based on the positional value principle:

To Decimal Number
\[N_{10} = \sum_{i=0}^{n-1} d_i \times b^i\]

Where b is the base and d_i is the digit at position i

From Decimal Number
\[N_b = \text{successive division by } b\]

Remainders give the digits from right to left

Conversion Formulas and Examples

General Positional Value System
\[N = d_n \times b^n + d_{n-1} \times b^{n-1} + \ldots + d_1 \times b^1 + d_0 \times b^0\]

Fundamental formula for all number systems with base b

Binary → Decimal Example
\[11110000_2 = 1×2^7 + 1×2^6 + 1×2^5 + 1×2^4 + 0×2^3 + 0×2^2 + 0×2^1 + 0×2^0\] \[= 128 + 64 + 32 + 16 + 0 + 0 + 0 + 0 = 240_{10}\]

Default value F0 (hex) equals 240 (decimal) and 11110000 (binary)

Hexadecimal → Decimal Example
\[F0_{16} = 15 \times 16^1 + 0 \times 16^0 = 240 + 0 = 240_{10}\]

F corresponds to 15 in the decimal system

Decimal → Other Systems (240 as Example)
→ Binary:
240 ÷ 2 = 120 remainder 0
120 ÷ 2 = 60 remainder 0
60 ÷ 2 = 30 remainder 0
30 ÷ 2 = 15 remainder 0
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Result: 11110000₂
→ Octal:
240 ÷ 8 = 30 remainder 0
30 ÷ 8 = 3 remainder 6
3 ÷ 8 = 0 remainder 3
Result: 360₈

→ Hex:
240 ÷ 16 = 15 remainder 0
15 ÷ 16 = 0 remainder 15(F)
Result: F0₁₆

Quick Reference

Default Value: 240
Binary: 11110000 Octal: 360 Decimal: 240 Hex: F0
More Examples
255 (FF hex):
Bin: 11111111
Oct: 377
100 (64 hex):
Bin: 1100100
Oct: 144
Hex Characters

A = 10

B = 11

C = 12

D = 13

E = 14

F = 15

Powers of Two

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64

2⁷ = 128

Number Systems - Detailed Description

Decimal Numbers (Base 10)

A decimal number is a number whose value is represented with the decimal digits 0 to 9. They are used in the decimal system, which has a base of 10. They are a fundamental concept in mathematics and everyday life.

Properties:
• Base 10 with digits 0-9
• Can represent whole and fractional numbers
• Decimal point for non-integer parts

Hexadecimal Numbers (Base 16)

The hexadecimal system uses base 16 and knows sixteen digits for representing numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. The digits 0 to 9 correspond to decimal values, while the letters A to F represent additional values.

Hexadecimal Prefixes

Hexadecimal numbers are often prefixed, e.g. 0x72 or $72. The hexadecimal system provides an efficient way to represent binary numbers, especially in the world of computers and programming.

Octal Numbers (Base 8)

The octal system uses base 8 and knows eight digits for representing a number: 0, 1, 2, 3, 4, 5, 6, 7. The digits in the octal system have the same value as in the decimal system. When counting in the octal system, the carry occurs after 7.

Applications:
• Computer technology (3 bits per octal digit)
• Unix file access permissions
• Compact binary representation

Binary Numbers (Base 2)

Binary numbers are the foundation for almost all modern computers and digital systems. They are used in the binary system, which only knows the digits 0 and 1. Unlike the decimal system, the binary system is limited to these two digits.

Digital Foundation

The binary system forms the basis for processing information in computers and other electronic devices. Each bit represents an electrical state: 0 = off, 1 = on.

Practical Application Examples

Binary System
  • Digital technology
  • Bit operations
  • Memory addresses
  • Logic circuits
Octal System
  • Unix permissions
  • Older computer systems
  • 3-bit grouping
  • Compact notation
Decimal System
  • Everyday mathematics
  • Science
  • Finance
  • Human intuition
Hexadecimal System
  • Programming
  • Memory addresses
  • Color codes (RGB)
  • Machine code
Conversion Tips
  • Binary ↔ Hex: 4 bits = 1 hex digit
  • Binary ↔ Octal: 3 bits = 1 octal digit
  • Remember powers: 2⁴=16, 2⁸=256, 2¹⁶=65536
  • Hex characters: A-F correspond to 10-15
  • Verification: Back-conversion for checking
  • Practice: Memorize small numbers


IT Functions

Decimal, Hex, Bin, Octal conversion • Shift bits left or right • Set a bit • Clear a bit • Bitwise AND • Bitwise OR • Bitwise exclusive OR

Special functions

Airy • Derivative Airy • Bessel-I • Bessel-Ie • Bessel-J • Bessel-Je • Bessel-K • Bessel-Ke • Bessel-Y • Bessel-Ye • Spherical-Bessel-J • Spherical-Bessel-Y • Hankel • Beta • Incomplete Beta • Incomplete Inverse Beta • Binomial Coefficient • Binomial Coefficient Logarithm • Erf • Erfc • Erfi • Erfci • Fibonacci • Fibonacci Tabelle • Gamma • Inverse Gamma • Log Gamma • Digamma • Trigamma • Logit • Sigmoid • Derivative Sigmoid • Softsign • Derivative Softsign • Softmax • Struve • Struve table • Modified Struve • Modified Struve table • Riemann Zeta

Hyperbolic functions

ACosh • ACoth • ACsch • ASech • ASinh • ATanh • Cosh • Coth • Csch • Sech • Sinh • Tanh

Trigonometrische Funktionen

ACos • ACot • ACsc • ASec • ASin • ATan • Cos • Cot • Csc • Sec • Sin • Sinc • Tan • Degree to Radian • Radian to Degree