If 'A' is a number in base-4 that equals 10 in decimal, what is 'A'?

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Question: If \'A\' is a number in base-4 that equals 10 in decimal, what is \'A\'?

Options:

Correct Answer: 22

Solution:

In base-4, \'22\' equals 2*4^1 + 2*4^0 = 8 + 2 = 10.

If 'A' is a number in base-4 that equals 10 in decimal, what is 'A'?

If 'A' is a number in base-4 that equals 10 in decimal, what is 'A'?

Step 1: Understand that base-4 means each digit represents a power of 4.
Step 2: Identify the digits in the base-4 number 'A'. Since we want 'A' to equal 10 in decimal, we need to find the correct digits.
Step 3: Start with the largest digit place in base-4. The first digit (from the right) is 4^0, the second is 4^1, and so on.
Step 4: To make 10 in decimal, we can try using two digits in base-4. Let's say 'A' is '22' in base-4.
Step 5: Calculate the decimal value of '22' in base-4: 2 * 4^1 + 2 * 4^0.
Step 6: Calculate 2 * 4^1 = 2 * 4 = 8.
Step 7: Calculate 2 * 4^0 = 2 * 1 = 2.
Step 8: Add the two results together: 8 + 2 = 10.
Step 9: Therefore, 'A' in base-4 that equals 10 in decimal is '22'.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-4 to decimal.
Place Value System – Recognizing the significance of each digit's position in a number based on its base.