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Digital Electronics: Numbering Systems

Most digital electronic circuits work with the binary number system. But what is a number system? A number system is simply a way of representing numeric values. Number systems use symbols called numerals to represent numeric quantities. The numerals 1, 2, and 3 represent the numeric quantities commonly known as one, two, and three.

In most number systems, numerals can be strung together to create larger numeric values, and the position of each numeral in the string determines its relative value. In the number 12, the numeral 1 represents the quantity ten, and the numeral 2 represents the quantity two. In the number 238, the numeral 2 represents the quantity two hundred, the numeral 3 represents the quantity thirty, and the numeral 8 represents the quantity eight.

You learned all this stuff in grade school, so it’s completely intuitive. Unfortunately, it’s so intuitive that it’s easy to miss its brilliance — and to overlook the fact that it’s completely arbitrary.

The fact that there are ten numerals in our everyday counting system — which is called the decimal system, or base 10 — is a simple result of the fact that humans have ten fingers. If humans had evolved with 12 fingers, we would’ve learned how to count in base 12.

Different number bases may seem strange, but you actually encounter them every day without thinking about it. One common example is the system used for keeping time. An hour contains 60 minutes, for example. You recognize that 1:30 is halfway between 1:00 and 2:00 without even thinking about it. You may not realize it, but you’re thinking in base 60 when you tell time.

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