base numbers


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 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

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