Octal Number System - mbits-mirafra/digitalDesignCourse GitHub Wiki

Octal number system:

  • A number system with base 8 is called an octal number system.

  • The octal number system uses 8 symbols, (0, 1, 2, 3, 4, 5, 6, 7) to represent the number.

Why Octal?

  • Old systems such as the UNIVAC 1050, PDP-8, ICL 1900 and IBM mainframes use Octal.

  • Octal was an ideal abbreviation of binary for these machines because their word size is divisible by three (each octal digit represents three binary digits).

  • Human errors are least while pronouncing as there are no alphabet symbols used.

  • Conversion from binary to octal is easier compared to hexadecimal and decimal.

  • Number of symbols are less in octal than hexa or decimal hence are human friendly to remember the symbols to greater extent.

Applications

  • Aircraft Transponders: In the early days of aviation, the transponder technology was developed using vacuum tube technology, which was limited in terms of the number of digits that could be displayed. Octal notation uses fewer digits than decimal or hexadecimal, which made it a more efficient way of encoding information for display purposes. Additionally, octal notation is easier to read and interpret quickly than hexadecimal, particularly for pilots and air traffic controllers who need to make quick decisions based on the information provided by the transponder.

While newer transponder systems can display information using decimal or hexadecimal notation, the use of octal remains a standard in aviation due to its historical significance and ease of use.

  • Digital displays: Octal numbers can be used to drive digital displays that use eight segments, such as some older calculators and clocks. Each segment represents a binary bit, and the octal number represents the binary pattern that should be displayed.

  • Assembly language programming: In computer programming, octal numbers can be used for bitwise operations and to represent memory addresses. Assembly language programs often use octal numbers to represent machine instructions and data.

  • Electrical engineering: Octal numbers can be used to represent bit patterns in digital circuits. For example, an 8-bit register can be represented using a two-digit octal number.

1. Octal to Decimal Conversion

2. Octal to Binary Conversion

3. Octal to Hexadecimal Conversion