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Represent the number 45.75 in the 48 bit words with 10 bits for the exponent under True Exponent method.

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Answer:

In the True Exponent method, the number is represented in the form:

(-1)^s * 1.fraction * 2^(exponent - bias)

For a 48-bit word with 10 bits for the exponent, the bias is 2^(10-1) - 1 = 511.

Let's represent 45.75 using the True Exponent method:

1. Convert 45.75 to binary:

45 (integer part) = 101101

0.75 (fractional part) = 0.11 (repeating)

So, the binary representation is 101101.11...

2. Normalize the binary representation:

Shift the point to the left until only one non-zero digit remains to the left of the point:

1.0110111... * 2^5

3. Calculate the exponent:

The exponent is 5, and with the bias of 511, the True Exponent representation of the exponent is 5 + 511 = 516, which in binary is 1000000100.

The final representation would be:

Sign bit (s) = 0 (positive)

Exponent (10 bits) = 1000000100

Fraction (remaining bits) = 0110111000...

Putting it all together: 0100000010011011000...

User Charlesdarwin
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