Base Angle Theorem
Definition of Base Angle Theorem
The Base Number is the basis of each place value column in a number system.
More About Base Angle Theorem
 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.
Video Examples: Base Numbers
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
Ques: Find the conversion of the decimal number 82 to base 6.
Choices:
A. 412 base 6B. 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.
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