Decimal Numbering System

Decimal Numbering System

The decimal numbering system should be familiar to everyone reading this book, because it's what you've been taught since early childhood. However, unless you love math, there are a few details that you might have forgotten about decimals that will help you better appreciate binary numbering; those details will be covered in this section.

Consider, for example, the number 235. The number is made up of three numerals2, 3, and 5. Numerals are simply symbols that represent a number; the word digit, short for decimal digit, is often used instead of numeral. For instance, 3 is the second digit of the number 235.

What does the number 235 really mean? Well, if you say the equivalent in English, you say something like "two-hundred thirty-five." To better appreciate how other numbering systemssuch as binarywork, consider a contrived and unusual expansion of the English language version of 235, as follows:

Two 100s, three 10s, and five 1s

It's a lot easier to say "two-hundred thirty-five" than "two 100s, three 10s, and five 1s." However, they both basically mean the same thing. You could even think of it in mathematical terms:

(2*100) + (3*10) + (5*1) = 235

Both the contrived English phrasing and the mathematical formula describe the core meaning of a multidigit decimal number. Each decimal digit represents its own value multiplied by a value associated with that digit's position in the number. It's more obvious with a table, such as Table B-1.