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Binary Numbers Tutorial

Binary Numbers Tutorial

Binary Numbers are represented by a series of binary digits which increase in powers of 2 from right to left

In this binary numbers tutorial we will see that binary digits called bits are written in base-2 so need two digits, zero and one. That is the binary numbering system we represent words and numbers using only the two digits 0 and 1.

There are different yet similar types of 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.

Binary Bits of Zeros and Ones

binary numbers bits

 

Binary Numbers Tutorial

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.

Digital Numbering System Comparison Table

Base, b Byte (8-bits) Word (16-bits)
Decimal 0
to
25510
0
to
65,53510
Binary 0000 0000
to
1111 11112
0000 0000 0000 0000
to
1111 1111 1111 11112
Hexadecimal 00
to
FF16
0000
to
FFFF16
Octal 000
to
3778
000 000
to
177 7778

We can see from the table above in this binary numbers tutorial 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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