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What is the decimal equivalent of 1110?1 point10121416

Question

What is the decimal equivalent of 1110?1 point10121416

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Solution

To convert the binary number 1110 to its decimal equivalent, follow these steps:

  1. Write down the binary number: 1110.

  2. Assign powers of 2 to each digit, starting from the rightmost digit (which is the least significant bit). The powers of 2 are as follows:

    • The rightmost digit (0) is 202^0.
    • The next digit to the left (1) is 212^1.
    • The next digit to the left (1) is 222^2.
    • The leftmost digit (1) is 232^3.
  3. Multiply each binary digit by its corresponding power of 2:

    • 1×23=1×8=81 \times 2^3 = 1 \times 8 = 8
    • 1×22=1×4=41 \times 2^2 = 1 \times 4 = 4
    • 1×21=1×2=21 \times 2^1 = 1 \times 2 = 2
    • 0×20=0×1=00 \times 2^0 = 0 \times 1 = 0
  4. Add the results of these multiplications together:

    • 8+4+2+0=148 + 4 + 2 + 0 = 14

Therefore, the decimal equivalent of the binary number 1110 is 14.

So, the correct answer is 14.

This problem has been solved

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