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(11110)2 = (1 × 24) + (1 × 23) + (1 × 22) + (1 × 21) + (0 × 20)

Question

(11110)2 = (1 × 24) + (1 × 23) + (1 × 22) + (1 × 21) + (0 × 20)

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Solution

Sure, here is the step by step conversion of the binary number (11110)2 to a decimal number:

  1. Multiply each digit of the binary number by 2 raised to the power of its position, starting from 0 on the right. The leftmost digit is multiplied by 2 raised to the power of n-1, where n is the total number of digits in the binary number.

  2. The binary number (11110)2 has 5 digits, so the leftmost digit is multiplied by 2 raised to the power of 4 (which is 16), the next digit is multiplied by 2 raised to the power of 3 (which is 8), and so on.

  3. So, the conversion is as follows:

    (1 × 2^4) + (1 × 2^3) + (1 × 2^2) + (1 × 2^1) + (0 × 2^0)

  4. Which simplifies to:

    (1 × 16) + (1 × 8) + (1 × 4) + (1 × 2) + (0 × 1)

  5. Adding these up gives:

    16 + 8 + 4 + 2 + 0 = 30

So, (11110)2 = 30 in decimal.

This problem has been solved

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