convert 1.75 to floating point representation

可以将 1.75 转换为 IEEE 754 浮点数表示法。首先，将 1.75 转换为二进制数，即 1.11。然后，确定符号位为 0，因为它是正数。接着，将小数点向左移动，使得整数部分为 1，即 0.111 × 2¹。然后将指数加上偏置值（127），得到 127 + 1 = 128，用 8 位二进制表示为 10000000。最后，将尾数部分填充为 23 位，即得到 001110 0000 0000 0000 0000 0000。因此，1.75 的 IEEE 754 浮点数表示为：0 10000000 00111000000000000000000。

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convert 1.75 to floating point representation IEEE 1958

Sure, I can help you with that.

To convert 1.75 to floating point representation IEEE 1958, we need to follow certain steps:

Step 1: Convert the decimal number 1.75 to binary.
1. Convert the integer part 1 to binary -> 1
2. Convert the fraction part 0.75 to binary:
0.75 x 2 = 1.5 (1 goes to the bit after the comma)
0.5 x 2 = 1 (1 goes to the next bit)
0

So 1.75 in binary is represented as 1.11

Step 2: Normalize the binary number
The binary number is normalized by moving the decimal point to the left so that there is only one non-zero digit before the decimal point. In this case, the binary number is already normalized.

Step 3: Determine the sign, exponent, and mantissa
Sign: Since the number is positive, the sign bit is 0.
Exponent: The exponent can be calculated using the formula:

exponent = (number of bits for exponent - 1) + bias

For IEEE 1958 floating point representation, the bias value is 127, and the number of bits for the exponent is 8.
In this case, the exponent is 0 + 127 = 127

Mantissa: The mantissa is the fractional part of the normalized binary number.
In this case, the mantissa is 1.11, which can be represented as:

1.11 = 1 + 1/2 + 1/4 = 1.5

The mantissa is then represented in binary as:

1.5 = 1.1000...

So the sign bit is 0, the exponent in binary is 01111111, and the mantissa in binary is 10000000000000000000000.

Putting it all together, 1.75 in floating point representation IEEE 1958 is:

0 11111111 10000000000000000000000

I hope this helps! Is there anything else I can assist you with?

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?