Binary to Octal Converter

Convert binary numbers to octal numbers, supporting large numbers and decimal points

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Binary Conversion

Binary to Octal

Octal to Binary

Input Value

Conversion Result

Not converted

Please input value and click convert button to see result

Usage Instructions

Select conversion type

Select is binary to octal or octal to binary.

Input value

Based on selected conversion type, input binary number (0 and 1) or octal number (0-7).

Click convert

Click convert button, system will automatically calculate and display conversion result.

Copy result

After conversion, you can click copy button to copy result to clipboard.

Binary and Octal conversion knowledge

Basic concept

Binary (Binary)

Binary is a base-2 numeral system that only uses 0 and 1 digits. It is the most basic data storage and processing mechanism in computers, as it's logic circuit only has two states: open(1) and close(0).

Octal (Octal)

Octal is a base-8 numeral system that uses digits from 0 to 7. Because of the 1-bit octal digit corresponds to 3-bit binary digit, it simplifies the representation of binary numbers, and is still used in some programming scenarios and system settings.

Conversion mechanism explanation

Binary to Octal conversion

Binary to Octal conversion uses grouping conversion method, the specific steps are as follows:

Group binary numbers from right to left every 3 bits
If the number of bits is less than 3, add 0 on the left
Convert each group of 3 bits to a corresponding 1 bit octal number

Example:

Binary: 110101 → Group: 110 101 → Convert: 6 5 → Octal: 65

Octal to Binary conversion

Octal to Binary conversion steps are as follows:

Convert each octal character to corresponding 3 bits binary number
Connect all binary numbers
Remove the leading zero (integer part) or trailing zero (fractional part)

Example:

Octal: 73 → Convert: 111 011 → Binary: 111011

Application scenario

UNIX/Linux系统

在UNIX和Linux系统中，文件权限通常用八进制数表示（如755），每一位代表一组权限。

嵌入式系统

在嵌入式编程中，八进制常用于表示寄存器配置和位操作，简化二进制数据的表示。

字符编码

在某些编程环境中，八进制转义序列用于表示特殊字符（如\012表示换行符）。

数据压缩

在某些数据压缩算法中，八进制用于表示编码表和压缩指令，提高压缩效率。

网络安全

在网络安全领域，八进制常用于表示某些网络地址和端口配置，简化安全规则设置。

硬件编程

在底层硬件编程中，八进制用于表示I/O端口地址和设备控制寄存器配置。

二进制-八进制对照表

Binary Number	Octal Number	Binary Number	Octal Number
000	0	100	4
001	1	101	5
010	2	110	6
011	3	111	7

Note: 3 binary bits correspond to 1 octal digit, which is the theoretical basis for quick conversion between the two.

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