**2.2 BASES AND NUMBER SYSTEMS**

The objective of this section is to introduce the various types of number representations used in digital system designs. The general method for numerical representation is called *positional number representation*. Consider the familiar decimal system. A number in decimal representation is made of digits that range from 0 to 9. Consider the following decimal number:

This number is normally written as *4261*, as the powers of 10 are implied by the position of that particular digit. Therefore, a decimal number *N* with *n* digits can be expressed as follows:

Decimal representations are said to be *base-10* or *radix-10 numbers* because each digit has 10 possible values, weighted as a power of 10, depending on the position of the digit in the number. In a similar way, in binary representation, each binary digit has two possible values, 1 and 0, and the digits are weighted as a power of 2, depending on their position in the number. The *binary system* of representation is also known as a *base-2 system*. Consider the following binary number:

Similarly, a binary number *N* with *n* digits can be expressed as follows:

In general, any number *N* can be represented in a base ...

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