In a certain numeral system, the digits used are 0, 1, 2, and 3. What is the dec

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Question: In a certain numeral system, the digits used are 0, 1, 2, and 3. What is the decimal equivalent of the number \'210\' in this system?

Options:

Correct Answer: 20

Solution:

\'210\' in base 4 is calculated as 2*4^2 + 1*4^1 + 0*4^0 = 32 + 4 + 0 = 36.

In a certain numeral system, the digits used are 0, 1, 2, and 3. What is the decimal equivalent of the number '210' in this system?

In a certain numeral system, the digits used are 0, 1, 2, and 3. What is the decimal equivalent of the number '210' in this system?

Step 1: Identify the base of the numeral system. In this case, the digits are 0, 1, 2, and 3, which means it is base 4.
Step 2: Write down the number '210' and identify the place values. The rightmost digit is the 'ones' place (4^0), the middle digit is the 'fours' place (4^1), and the leftmost digit is the 'sixteens' place (4^2).
Step 3: Calculate the value of each digit by multiplying it with its corresponding power of 4. For '210':
Step 4: Calculate the leftmost digit: 2 * 4^2 = 2 * 16 = 32.
Step 5: Calculate the middle digit: 1 * 4^1 = 1 * 4 = 4.
Step 6: Calculate the rightmost digit: 0 * 4^0 = 0 * 1 = 0.
Step 7: Add all the values together: 32 + 4 + 0 = 36.
Step 8: The decimal equivalent of '210' in base 4 is 36.

Base Conversion – Understanding how to convert numbers from one base (in this case, base 4) to decimal (base 10) by using the positional value of each digit.