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 110010012 is equivalent to 20110
    The binary number 1101002 can be converted into decimal number as:
    1101002 = 1 � 25 + 1 � 24 + 0 � 23 + 1 � 22 + 0 � 21 + 0 � 20
    = 32 + 16 + 0 + 4 + 0 + 0
    = 52
    So, the decimal equivalent of 1101002 is equivalent to 5210.

Solved Example on Base Numbers

Ques: 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.

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