A number in hexadecimal form is represented as A189B. What is the number in decimal?

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justaguide eNotes educator| Certified Educator

Decimal refers to numbers written in base 10. These have the digits 0,1,2,3,4,5,6,7,8 and 9. Hexadecimal refers to base 16. In addition to the digits used to write decimal numbers, 5 additional digits are used, A, B, C, D, E, F. These digits represent the decimal numbers 10, 11, 12, 13, 14 and 15.

When a number is written in any base b, its right-most digit has a value equal to the digit multiplied by b^0. As we move towards the left, each digit has to be multiplied by the base raised to power one more than the previous digit.

The hexadecimal number A189B is equal to:

11*16^0 + 9*16^1 + 8*16^2 + 1*16^3 + 10*16^4

= 11 + 144 + 2048 + 4096 + 655360

= 661659

The hexadecimal number `(A189B)_16 = (661659)_10`