Decimal Numbering: 1s, 10s, and 100s Digits
|
Value Associated with That Digit or
Column |
100 |
10 |
1 |
|
The digits |
2 |
3 |
5 |
With decimal numbering, the right-most digit in a number
represents a value of that digit times 1; the second from the right represents
the value of the digit times 10; and the third from the right represents a value
of that digit times 100. This same logic continues for larger numbers, with each
successive digit to the left having a value 10 times the digit to its right. In
this example, the 5 means 5 times 1 because it's in the 1s column. Similarly,
the single digit in the 10s column represents 3 times 10. Finally, the 2 in the
100s digit column means 2 times 100.
With decimal, each digit, going right-to-left, represents a
multiple of an increasing power of 10. The rightmost digit of a decimal number
lists the number of 1s, if you will, because 100 = 1. That digit is
called the 1s digit. The second digit from
the right is the number of 10s, called the 10s digit, because
101 = 10; the third from the right is the 100s
digit, because 102 = 100; and so on.
Because you've used it all your life, the math is probably so
intuitive that you really don't need to think about it to this depth. However,
thinking about decimal in this way will help you appreciate binary. For
instance, decimal numbering works with the 1s, 10s, and 100s digits because you
only have 10 numerals to work with0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If you count
starting at 0, after you reach 9, you're out of numerals; there is no single
symbol or numeral that represents the idea behind the number 10. So, to write
down a number bigger than 9, you need at least two digitsone that represents a
multiple of 10 and another that represents a multiple of 1.
Next, you'll see how binary numbering works on the same basic
premise, but with just two numerals or digits.
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