Binary Numbers Tutorial

There are different yet similar binary numbering systems used in digital electronic circuits and computers.

However, the numbering system used in one type of circuit may be different to that of another type of circuit, for example, the memory of a computer would use hexadecimal numbers while the keyboard uses decimal numbers.

Then the conversion from one number system to another is very important with the four main forms of arithmetic being.

  • Decimal – The decimal numbering system has a base of 10 (MOD-10) and uses the digits from 0 through 9 to represent a decimal number value.
  • Binary – The binary numbering system has a base of 2 (MOD-2) and uses only two digits a “0” and a “1” to represent a binary number value.
  • Octal – The octal numbering system has a base of 8 (MOD-8) and uses 8 digits between 0 and 7 to represent an octal number value.
  • Hexadecimal – The Hexadecimal numbering system has a base of 16 (MOD-16) and uses a total of 16 numeric and alphabetic characters to represent a number value. Hexadecimal numbers consist of digits 0 through 9 and letters A to F.

Long binary numbers are difficult to both read or write and are generally converted into a system more easily understood or user friendly. The two most common derivatives based on binary numbers are the Octal and the Hexadecimal numbering systems, with both of these limited in length to a byte (8-bits) or a word (16-bits).

Octal numbers can be represented by groups of 3-bits and hexadecimal numbers by groups of 4-bits together, with this grouping of the bits being used in electronic or computer systems in displays or printouts. The grouping together of binary numbers can also be used to represent Machine Code used for programming instructions and control such as an Assembly Language.

Comparisons between the various Decimal, Binary, Hexadecimal and Octal numbers are given in the following table.

Comparison Table

Base, b Byte (8-bits) Word (16-bits)
Decimal 0
Binary 0000 0000
1111 11112
0000 0000 0000 0000
1111 1111 1111 11112
Hexadecimal 00
Octal 000
000 000
177 7778

We can see from the table above that the Hexadecimal numbering system uses only four digits to express a single 16-bit word length, and as a result it is the most commonly used Base Numbering System for digital, micro-electronic and computer systems.


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  • H
    Harsh Joshi

    This give me some knowledge

  • h
    handsen mulenga

    The tutorials are wonderful and great, thank you so much on these on the AND gate how I wish I could see more circuits on these other gates as well as boolean algebra

  • N
    Nancy Nakan

    Thanks so much about these notes about how to convert and I wish I would see some more examples of how to concert Binary to Decimal, Octadecimal.

  • e

    converting binary number to decimal and show calculations

    • B
      Billy Shope

      Starting at left, it’s 1-3-7-14-29-59-119-238-476-953-1907

      So, 1907 is the decimal equivalent of the binary 11101110011

  • S
    Shrikant S. Kamble

    Good notes for beginners.

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