Binary Number System
The binary number system is a base-2 number system that uses only two digits, 0 and 1, to represent any value. Each digit in a binary number represents a power of 2, with the rightmost digit representing 2^0 (1), the next digit to the left representing 2^1 (2), and so on. To convert a binary number to a decimal number, we multiply each digit by the corresponding power of 2 and add up the results.
For example, the binary number 1011 can be converted to a decimal number as follows:
1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 8 + 0 + 2 + 1 = 11
Binary numbers are used extensively in digital electronics and computer programming because they can be easily represented using electronic switches, and they are the fundamental building blocks of digital circuits.
Octal Number System
The octal number system is a base-8 number system that uses the digits 0-7 to represent any value. Each digit in an octal number represents a power of 8, with the rightmost digit representing 8^0 (1), the next digit to the left representing 8^1 (8), and so on. To convert an octal number to a decimal number, we multiply each digit by the corresponding power of 8 and add up the results.
For example, the octal number 23 can be converted to a decimal number as follows:
2 * 8^1 + 3 * 8^0 = 16 + 3 = 19
Octal numbers are used less frequently than binary numbers in digital electronics and computer programming, but they are still useful in certain contexts. For example, octal numbers are often used to represent file permissions in Unix-based operating systems.
Relationship Between Binary and Octal
Binary and octal are related because each octal digit corresponds to three binary digits. This is because 2^3 = 8, so each group of three binary digits can be represented by a single octal digit.
To convert a binary number to an octal number, we can simply group the binary digits into groups of three, starting from the rightmost digit, and convert each group to an octal digit. For example, the binary number 101110110 can be converted to an octal number as follows:
| 1 | 011 | 101 | 110 |
|---|---|---|---|
| 1 | 3 | 5 | 6 |
Therefore, the octal representation of the binary number 101110110 is 1356.
To convert an octal number to a binary number, we can simply convert each octal digit to a group of three binary digits. For example, the octal number 127 can be converted to a binary number as follows:
| 1 | 2 | 7 |
|---|---|---|
| 001 | 010 | 111 |
Therefore, the binary representation of the octal number 127 is 001010111.
Converting between binary and octal is relatively simple because each octal digit corresponds to three binary digits. To convert a binary number to an octal number, we can group the binary digits into groups of three starting from the rightmost digit and convert each group to an octal digit. To convert an octal number to a binary number, we can simply convert each octal digit to a group of three binary digits.
In conclusion, binary and octal are two different number systems that are commonly used in digital electronics and computer programming. While binary is the more commonly used number system, octal is still useful in certain contexts, such as representing file permissions in Unix-based operating systems. The relationship between binary and octal is straightforward, with each octal digit corresponding to three binary digits, making it easy to convert between the two number systems.
Table of Binary:
Here is a table showing the correspondence of binary, hexadecimal, decimal, octal, and text:
| Binary | Hexadecimal | Decimal | Octal | Text |
|---|---|---|---|---|
| 00000000 | 0x00 | 0 | 0 | NUL |
| 00000001 | 0x01 | 1 | 1 | SOH |
| 00000010 | 0x02 | 2 | 2 | STX |
| 00000011 | 0x03 | 3 | 3 | ETX |
| 00000100 | 0x04 | 4 | 4 | EOT |
| 00000101 | 0x05 | 5 | 5 | ENQ |
| 00000110 | 0x06 | 6 | 6 | ACK |
| 00000111 | 0x07 | 7 | 7 | BEL |
| 00001000 | 0x08 | 8 | 10 | BS |
| 00001001 | 0x09 | 9 | 11 | HT |
| 00001010 | 0x0A | 10 | 12 | LF |
| 00001011 | 0x0B | 11 | 13 | VT |
| 00001100 | 0x0C | 12 | 14 | FF |
| 00001101 | 0x0D | 13 | 15 | CR |
| 00001110 | 0x0E | 14 | 16 | SO |
| 00001111 | 0x0F | 15 | 17 | SI |
| 00010000 | 0x10 | 16 | 20 | DLE |
| 00010001 | 0x11 | 17 | 21 | DC1 |
| 00010010 | 0x12 | 18 | 22 | DC2 |
| 00010011 | 0x13 | 19 | 23 | DC3 |
| 00010100 | 0x14 | 20 | 24 | DC4 |
| 00010101 | 0x15 | 21 | 25 | NAK |
| 00010110 | 0x16 | 22 | 26 | SYN |
| 00010111 | 0x17 | 23 | 27 | ETB |
| 00011000 | 0x18 | 24 | 30 | CAN |
| 00011001 | 0x19 | 25 | 31 | EM |
| 00011010 | 0x1A | 26 | 32 | SUB |
| 00011011 | 0x1B | 27 | 33 | ESC |
| 00011100 | 0x1C | 28 | 34 | FS |
List of Binary:
Here's a list of hundred binary numbers:
How to use
- First, you have to enter any Binary or Octal number that you want to convert to Octal or Binary and then click the convert button.
- As soon as you click the convert button, your data will be displayed below.
- You can copy any data you want to copy by pressing the copy button below the tool.
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