Binary Numbers Summary |
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Binary Numbers Summary
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
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 |
It can be seen from the above table 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 Binary Numbering System for
electronic and micro-electronic systems.
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