Using the IEEE 754 floating point format, write down the bit pattern that would represent −1/4. Can you represent −1/4 exactly?
时间: 2024-05-20 07:17:36 浏览: 12
The bit pattern that represents -1/4 in IEEE 754 floating point format is:
1 10000000 10000000000000000000000
This bit pattern represents a negative number (-1), with an exponent of -2 (10000000 = 128 + 0 = 128, 128 - 127 = 1, -2 = 2^-2), and a significand of 0.5 (10000000000000000000000 = 1 + 0.25 = 1.25, 1.25 - 1 = 0.25).
This representation is not exact, as the significand is rounded to the nearest representable value in binary. The closest representable value to -1/4 is actually -0.25, which has the same exponent and a significand of 0.01. Therefore, the actual value represented by this bit pattern is -0.25, not exactly -1/4.
相关问题
What decimal number does the bit pattern 0x0C000000 represent if it is a floating point number? Use the IEEE 754 standard.
The bit pattern 0x0C000000 represents a floating point number in hexadecimal format.
To convert it to decimal using the IEEE 754 standard, we need to break down the bits into their respective parts:
1. The first bit is the sign bit, with a value of 0, indicating that the number is positive.
2. The next 8 bits represent the exponent, which is biased by 127. In this case, the exponent bits are 0xC0, which is equal to 192 in decimal. Subtracting the bias of 127 gives us an actual exponent of 65.
3. The remaining 23 bits represent the significand or mantissa, with an implied leading 1. In this case, the significand bits are 0x000000, which means the actual significand is 1.
Putting it all together, we get:
(-1)^0 * 1 * 2^(65-127) = 2^(-62) = 0.0000000000000000000000000000000000000000000000000000000015625
Therefore, the decimal number represented by the bit pattern 0x0C000000 in IEEE 754 floating point format is approximately 0.0000000000000000000000000000000000000000000000000000000015625.
convert 1.75 to IEEE 1958 floating point representation given 1 bit for sign,5 bit for exponent,7 for mantissa
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?
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