convert 1.75 to IEEE 1958 floating point representation given 1 bit for sign,5 bit for exponent,7 for mantissa
时间: 2024-05-23 13:14:59 浏览: 8
Sure, I understand your question. To convert 1.75 to IEEE 1958 floating point representation with 1 bit for sign, 5 bits for exponent and 7 bits for mantissa, we need to follow a few steps.
Firstly, we need to represent 1.75 in binary form:
1 = 1 (in binary form)
0.75 = 1 * (0.5)^1 + 1 * (0.5)^2
= 0.11 (in binary form)
Therefore, 1.75 in binary form is 1.11.
Next, we need to determine the sign, exponent and mantissa for this number.
The sign bit will be 0 as 1.75 is a positive number.
The exponent is calculated by adding the bias, which is 15 ((2^5)/2 - 1), to the binary exponent equivalent of 1.75.
The binary exponent equivalent is 1 (as 1.11 has 1 digit before the decimal point).
Therefore, the exponent is 16 (15+1) and we need to represent 16 in binary form using 5 bits which is 10000.
The mantissa is the fractional part of the binary representation of 1.75, which is 11.
So, the IEEE 1958 floating point representation of 1.75 with 1 bit for sign, 5 bit for exponent, and 7 bits for mantissa is:
0 | 10000 | 1100000
where the first bit is the sign bit (0 for positive), the next 5 bits are the exponent (10000 which is 16 in decimal), and the last 7 bits are the mantissa (1100000 which is 96 in decimal).
I hope that helps! Do you have any other questions?