What is the base 10 representation of 1110?

Answer 1

The base 10 representation of 1110 is 110^3 + 110^2 + 110^1 + 010^0, which simplifies to 1000 + 100 + 10 + 0, resulting in 1110 in base 10. In other words, each digit in the number is multiplied by a power of 10 based on its position in the number, and then these products are added together to get the base 10 representation.

Answer 2

You have given no base for the 1110, so you'll have to do the conversion yourself by writing the place column values over the digits:

1. write 1 over the rightmost digit.
2. start with the digit to the left of the rightmost digit:
3. write the value over the digit to the right of the current digit multiplied by the base over the digit
4. move left one digit
5. if you have not run out of digits repeat from step 3.

Now that you have written the place column values, the number 1110 (in whatever base it is) can be converted to base 10 by summing all the digits of the number multiplied by the place column value over it.

eg if 1110 is in octal (base 8), this gives:

512___64___8___1

_1______1___1___0

→ 1110 base 8 = 512 × 1 + 64 × 1 + 8 × 1 + 1 × 0 = 512 + 64 + 8 = 584 in base 10.

If the 1110 is not in base 8, you'll have to do the conversion yourself.

You may notice that the place column value are 8 to the power of the number of columns to the left of the ones column:

512 = 8³

64 = 8²

8 = 8¹

1 = 8⁰

→ 512__64__8__1 place column values are 8³__8²__8¹__8⁰

This is true of any base, eg base 10:

10³__10²__10¹__10⁰ is equivalent to 1000__100__10__1

so 1234 would be 1 × 1000 + 2 × 100 + 3 × 10 + 4 × 1.