** Definition of Base Numbers **

- The Base Number is the basis of each place value column in a number system.

**More about Base Numbers**

- In a place value system, each column contains digits representing successive powers of the base number.
- In a decimal system, the base number is 10.

**Examples of Base Numbers **

- The binary number 11001001
_{2}is equivalent to 20110. - The binary number 110100
_{2}can be converted into decimal number as:

110100_{2}= 1 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 0 × 20

= 32 + 16 + 0 + 4 + 0 + 0

= 52

So, the decimal equivalent of 110100_{2}is equivalent to 52_{10}.

**Solved Example on Base Numbers**

Find the conversion of the decimal number 82 to base 6.

Choices:

A. 412 base 6

B. 142 base 6

C. 214 base 6

D. 224 base 6

Correct Answer:C

Solution:

Step 1:82 divided by 6 leaves the remainder 4.

Step 2:Again the quotient 13 divided by 6 leaves the remainder 1.

Step 3:Once again, the quotient 2 divided by 6 leaves the remainder 2.

Step 4:The answer is formed by taking the remainders in reverse order: 214 base 6.

**Related terms for Base Numbers**

- Base
- Binary System
- Decimal System
- Number System
- Place Value