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What is "base-2 number system"?


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49 minutes ago, PeterBushMan said:

Binary is a base-2 number system that uses two states 0 and 1 to represent a number.


Does it mean it only use 2 digits.

So decimal is a bse-10 number system.



Not quite.

Yes binary is a base 2 number representation system.

But no, it does not use 2 states on their own to represent a number.

That could only ever represent 2 numbers.

A number system are designed to represent all the numbers in its particular range.

In order to do this you can either use a different symbol for every number, which is obviously inefficient and difficult to learn.

Or you can repeat symbols in some way, with each repetition having a different meaning.

The smallest count of symbols you need to do this is called is 2 and is called binary.

2 is then called the base.

One consequence of using 2 is that it leads to very long representations of numbers, both numerically bigger numbers and fractions.

In general, The larger the count of symbols the shorter the repreentation becomes.

So if use use 3 symbols we get ternary numbers, also called trinary numbers

So if use use 4 symbols we get quaternary numbers

So if use use 5 symbols we get quinary numbers

So if use use 6 symbols we get seximal numbers

So if use use 7 symbols we get septernary numbers

So if use use 8 symbols we get octal numbers  - note this one does not follow the pattern and is abused by computer science to also mean groupings of binary numbers.

So if use use 9 symbols we get nonnary numbers

So if use use 10 symbols we get denary numbers commonly, but wrongly, called 'decimal numbers'.

So if use use 16 symbols we get hexadecimal numbers or hex numbers.


Mixed representations can also be used, such as BCD or binary coded decimal and octal.

Up to and including base 10 we use the 10 digits 1 through 9 and zero as the symbols

To additional obtain symbols for number systems with a base greater than 10, we use letters from the Latin alphabet, eg hex numbers use the 6 letters A,B,C,D,E and F.


Does this help ?




Edited by studiot
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11, our standar "decimal system"  is base 10.  We have 10 digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and create all numerals using those.  For example immediately  after "9" is 10= 1*10+ 0, then 11= 1*10+ 1,  then 12= 1*10+ 2, etc.

In "binary" we have only two digits, 0 and 1 and create all numerals using the. For example immediately after 1 is 10 which can be read as "2 and 0", then 11= 2+ 1= 3, then 100= 4+0*2+ 0*1, then 101= 4+ 0*2+ 1*1= 5, then 110= 4+ 1*2+ 0*1, etc.

Notice that, just as 10,100, 1000, 10000 are "powers of 10" so in binary, 10= 2, 100= 4, 1000= 8 are "powers of 2".

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