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Convert the binary number 10112 to decimal.

Computer Science

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Answer

81588\sqrt{158}

Step-by-step solution

10 steps

  1. Check if 10112 is even.

    10112÷2=505610112 \div 2 = 5056

  2. Check if 5056 is even.

    5056÷2=25285056 \div 2 = 2528

  3. Check if 2528 is even.

    2528÷2=12642528 \div 2 = 1264

  4. Check if 1264 is even.

    1264÷2=6321264 \div 2 = 632

  5. Check if 632 is even.

    632÷2=316632 \div 2 = 316

  6. Check if 316 is even.

    316÷2=158316 \div 2 = 158

  7. Check if 158 is even.

    158÷2=79158 \div 2 = 79

  8. 79 is a prime number (not divisible by 2, 3, 5, or 7).

    Prime factorization:

    10112=27×7910112 = 2^7 \times 79

  9. Rewrite for square root.

    10112=27×79=26×2×79=(23)2×158\sqrt{10112} = \sqrt{2^7 \times 79} = \sqrt{2^6 \times 2 \times 79} = \sqrt{(2^3)^2 \times 158}

  10. Simplify.

    10112=23158=8158\sqrt{10112} = 2^3 \sqrt{158} = 8\sqrt{158}

    8\sqrt{158}

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