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Decimal Numbering: 1s, 10s, and 100s Digits
Nov 26,2008 00:00
by
alperen
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. |