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Decimal to Binary conversion of (164) 2

Mathematics

ScanSolve AI Answer

Answer

10100100210100100_2

Step-by-step solution

8 steps

The image shows the process of converting the decimal number 16410164_{10} to its binary equivalent using repeated division by 2.

Let's verify the steps shown in your work:

  1. Divide 164 by 2.

    164÷2=82164 \div 2 = 82 with a remainder of 0. (Correct)

  2. Divide 82 by 2.

    82÷2=4182 \div 2 = 41 with a remainder of 0. (Correct)

  3. Divide 41 by 2.

    41÷2=2041 \div 2 = 20 with a remainder of 1. (Correct)

  4. Divide 20 by 2.

    20÷2=1020 \div 2 = 10 with a remainder of 0. (Correct)

  5. Divide 10 by 2.

    10÷2=510 \div 2 = 5 with a remainder of 0. (Correct)

  6. Divide 5 by 2.

    5÷2=25 \div 2 = 2 with a remainder of 1. (Correct)

  7. Divide 2 by 2.

    2÷2=12 \div 2 = 1 with a remainder of 0. (Correct)

  8. Divide 1 by 2.

    1÷2=01 \div 2 = 0 with a remainder of 1. (Correct)

    To obtain the binary number, you read the remainders from bottom to top.
    The remainders are: 1,0,1,0,0,1,0,01, 0, 1, 0, 0, 1, 0, 0.

    Therefore, the correct binary representation of 16410164_{10} is 10100100210100100_2.

    Your division steps are all correct. However, the final binary number you wrote on the right side of the page, (0010010)2(0010010)_2, is incorrect. It seems you might have missed the leftmost '1' and reversed the order of some digits.

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