Question

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

Answer 1

Answer:

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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