If a number in base 4 is represented as '210', what is its equivalent in base 10

If a number in base 4 is represented as '210', what is its equivalent in base 10?

If a number in base 4 is represented as '210', what is its equivalent in base 10?

Step 1: Understand that '210' is a number in base 4.
Step 2: Identify the place values for each digit in '210'. The rightmost digit is the 0th place, the next is the 1st place, and the leftmost is the 2nd place.
Step 3: Write down the base 4 values for each digit: 2 is in the 2nd place, 1 is in the 1st place, and 0 is in the 0th place.
Step 4: Calculate the value of each digit by multiplying it with 4 raised to the power of its place value: 2 * 4^2, 1 * 4^1, and 0 * 4^0.
Step 5: Calculate each term: 2 * 4^2 = 2 * 16 = 32, 1 * 4^1 = 1 * 4 = 4, and 0 * 4^0 = 0 * 1 = 0.
Step 6: Add all the calculated values together: 32 + 4 + 0 = 36.
Step 7: The equivalent of '210' in base 4 is 36 in base 10.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base 4 to base 10.
Exponentiation – Applying the correct powers of the base when converting each digit of the number.