We are very familiar with counting in the decimal system.
This means that we have numbers from one to nine and then go on to a number of
tens.
Binary numbers are used for these sampled values.
Binary is a way of
expressing numbers in ones (high voltage value) or zeros (low voltage value) – there is
nothing in between. You can only have either a 1 or a 0.
In mathematical language
you are expressing numbers to the base 2 instead of our normal decimal system where we
use the base 10.
Decimal number | Binary equivalent | Decimal number | Binary equivalent |
0 | 0000 | 8 | 1000 |
1 | 0001 | 9 | 1001 |
2 | 0010 | 10 | 1010 |
3 | 0011 | 11 | 1011 |
4 | 0100 | 12 | 1100 |
5 | 0101 | 13 | 1101 |
6 | 0110 | 14 | 1110 |
7 | 0111 | 15 | 1111 |
The number
of digits in the group gives is the BIT NUMBER. For example all the above numbers are
FOUR BIT NUMBERS – there are only four ones or zeros. You can see from the table that
four bit binary numbers can only deal with numbers up to decimal 15. If we want to express
larger numbers we have to have 8 bit, 16 bit or 32 bit binary numbers. Many of your
computers are 32 BIT machines – they deal with numbers
like:
00110011010011100011000110101011
The table below shows some
examples of converting some decimal numbers into binary:
Decimal | Thirty two | Sixteen | Eight | Four | Two | One | Binary |
27 | 0 | 1 | 1 | 0 | 1 | 1 | 011011 |
53 | 1 | 1 | 0 | 1 | 0 | 1 | 110101 |
62 | 1 | 1 | 1 | 1 | 1 | 0 | 111110 |
In a computer the ones and zeros are sent in a string with
one following the other so a 32 bit number is a longish string – longer than a four bit
number.
Computers and other such machines can understand binary numbers
because there are only two options – ON (1) or OFF (0).
Binary number | Decimal equivalent | Binary number | Decimal equivalent | |
00011110 | 30 | 01010010 | 82 | |
00100011 | 35 | 001010011 | 83 | |
00100100 | 36 | 01011100 | 92 | |
00101110 | 46 | 01100010 | 98 | |
0011100 | 56 | 01101000 | 104 | |
00011110 | 60 | 01101110 | 110 | |
00111110 | 62 | 01110011 | 115 | |
01000001 | 65 | 01110100 | 116 | |
01000111 | 71 | 01110000 | 120 | |
01001000 | 72 | 10000010 | 130 | |
01001011 | 75 | 10110111 | 187 | |
01001100 | 76 | 11000111 | 203 | |
01001110 | 78 | 11001111 | 211 | |
01010000 | 80 | 11110100 | 248 |
But having explained how binary numbers relate to decimal
numbers we must look at why binary numbers are so useful — especially in digital devices
such as computers and in transmitting digital information in CDs, TVs, cameras
etc.
The point is that binary numbers are made up of ones and noughts as you can
see from looking at the table. If we 'translate' this into electricity we could have a circuit that
is either
ON or OFF or a voltage that is either HIGH or LOW (the low being
zero).
The real advantage of a binary system is that the voltages need not be
exactly nought or one to give a meaningful output.
Look at the people with the flags. Let's imagine that a flag
held upright means a one and a flag held horizontal means a zero. So the number
represented would be 11010110 in binary.
But if you look carefully you will see that
person three does not have their flag quite horizontal and person seven does not have theirs
quite vertical. However they are still close enough for us to take them as a 0 and a
1.
In a digital signal using binary code the output will be interpreted as a perfect
version of the input even if some of the voltages are not quite exact just like the
flags.