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...