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11 December, 01:00

What is the largest positive number one can represent in an eight-bit 2's complement code? Write your result in binary and decimal.

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  1. 11 December, 03:17
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    The largest positive number one can represent in an eight-bit 2's complement code is 01111111.

    Explanation:

    It is displayed as 01111111₂ in Binary.

    To derive its decimal equivalent, we have to convert the binary code into decimal as follows:

    01111111₂ = 0 * 2⁷ + 1 * 2 ⁶ + 1 * 2⁵ + 1 * 2⁴ + 1 * 2³ + 1 * 2² + 1 * 2¹ + 1 * 2⁰

    = 0 + 64 + 32 + 16 + 8 + 4 + 2 + 1

    = 127

    Therefore, the decimal equivalent is 127.
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