Question

Convert the following number to base 10:
11002 = ?10

Answer 1

The binary number 11002 converts to the base 10 number 1210 by calculating the sum of each digit multiplied by the corresponding power of 2 based on its position.

Step-by-step explanation:

To convert the binary number 11002 to base 10, we can start by assigning each digit a power of 2 based on its position, starting from the right and beginning with 20. These positions represent 23, 22, 21, and 20 respectively. To calculate the value, you sum the products of each binary digit multiplied by its corresponding power of 2.

Here's the breakdown:
(1 × 23) + (1 × 22) + (0 × 21) + (0 × 20)
(1 × 8) + (1 × 4) + (0 × 2) + (0 × 1)
8 + 4 + 0 + 0 = 12

Therefore, 11002 in binary is equal to 1210 in base 10.