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If the base-2 number 1101 is converted to base-10, what is the result?

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Question: If the base-2 number 1101 is converted to base-10, what is the result?

Options:

  1. 13
  2. 11
  3. 14
  4. 12

Correct Answer: 13

Solution: 

To convert from base-2 to decimal, calculate 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8 + 4 + 0 + 1 = 13.

If the base-2 number 1101 is converted to base-10, what is the result?

Practice Questions

Q1
If the base-2 number 1101 is converted to base-10, what is the result?
  1. 13
  2. 11
  3. 14
  4. 12

Questions & Step-by-Step Solutions

If the base-2 number 1101 is converted to base-10, what is the result?
  • Step 1: Write down the base-2 number: 1101.
  • Step 2: Identify the position of each digit from right to left, starting at 0: 1(3), 1(2), 0(1), 1(0).
  • Step 3: Calculate the value of each digit by multiplying it by 2 raised to the power of its position: 1*2^3, 1*2^2, 0*2^1, 1*2^0.
  • Step 4: Calculate each term: 1*2^3 = 8, 1*2^2 = 4, 0*2^1 = 0, 1*2^0 = 1.
  • Step 5: Add all the calculated values together: 8 + 4 + 0 + 1.
  • Step 6: The final result is 13.
  • Binary to Decimal Conversion – Understanding how to convert a binary number (base-2) to its decimal equivalent (base-10) using powers of 2.
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