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    Decimal equivalent of 111111 is:
    Question

    Decimal equivalent of 111111 is:

    A.

    59

    B.

    57

    C.

    65

    D.

    63

    Correct option is D

    To convert the binary number 111111 to its decimal equivalent, we sum the powers of 2 for each bit that is set to 1.The binary number 1111112 can be expanded as follows:1111112=125+124+123+122+121+120Calculating each term:125=32124=16123=8122=4121=2120=1Adding these values together:32+16+8+4+2+1=63Therefore, the decimal equivalent of 111111 is 63.The correct answer is (d) 63.\text{To convert the binary number 111111 to its decimal equivalent, we sum the powers of 2 for each bit that is set to 1.} \\\\\text{The binary number } 111111_2 \text{ can be expanded as follows:} \\\\111111_2 = 1 \cdot 2^5 + 1 \cdot 2^4 + 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \\\\\text{Calculating each term:} \\1 \cdot 2^5 = 32 \\1 \cdot 2^4 = 16 \\1 \cdot 2^3 = 8 \\1 \cdot 2^2 = 4 \\1 \cdot 2^1 = 2 \\1 \cdot 2^0 = 1 \\\\\text{Adding these values together:} \\32 + 16 + 8 + 4 + 2 + 1 = 63 \\\\\text{Therefore, the decimal equivalent of } 111111 \text{ is } 63. \\\\\text{The correct answer is (d) 63.}​​

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