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In a certain numeral system, the digits are represented as follows: 0, 1, 2, 3,

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Question: In a certain numeral system, the digits are represented as follows: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B. What is the decimal equivalent of \'B2\'?

Options:

  1. 10
  2. 12
  3. 14
  4. 16

Correct Answer: 14

Solution: 

\'B2\' in this system is 11*12^1 + 2*12^0 = 132 + 2 = 134 in decimal.

In a certain numeral system, the digits are represented as follows: 0, 1, 2, 3,

Practice Questions

Q1
In a certain numeral system, the digits are represented as follows: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B. What is the decimal equivalent of 'B2'?
  1. 10
  2. 12
  3. 14
  4. 16

Questions & Step-by-Step Solutions

In a certain numeral system, the digits are represented as follows: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B. What is the decimal equivalent of 'B2'?
  • Step 1: Identify the base of the numeral system. In this case, the digits are 0-9 and A-B, which means the base is 12.
  • Step 2: Break down the number 'B2' into its individual digits. 'B' is the first digit and '2' is the second digit.
  • Step 3: Convert each digit to its decimal value. 'B' represents 11 in decimal, and '2' remains 2.
  • Step 4: Determine the position of each digit. 'B' is in the 12^1 place (the left position) and '2' is in the 12^0 place (the right position).
  • Step 5: Calculate the value of 'B' in decimal: 11 * 12^1 = 11 * 12 = 132.
  • Step 6: Calculate the value of '2' in decimal: 2 * 12^0 = 2 * 1 = 2.
  • Step 7: Add the two values together: 132 + 2 = 134.
  • Step 8: The decimal equivalent of 'B2' is 134.
  • Base Conversion – Understanding how to convert numbers from one numeral system to another, specifically from a base-12 system to decimal.
  • Digit Representation – Recognizing the representation of digits in a non-decimal numeral system, including the use of letters for values greater than 9.
  • Positional Value – Calculating the value of each digit based on its position in the number, using powers of the base.
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