Solve IEEE Floating Point Format (32bits) for N=-1552.225

[teng125]

code n=-1552.225 into IEEE floating point format (32bits)
anybody knows how to solve this??
is it possible to solve it??

 

[chroot]

Have you tried looking up the IEEE floating point format (IEEE 754)?

http://en.wikipedia.org/wiki/IEEE_floating-point_standard

- Warren

 

[piercas]

Yes, it is possible to solve this. The IEEE floating-point format is a standardized way of representing numbers in binary form, which is commonly used in computer systems. This format uses 32 bits to represent a number, with a specific structure that includes a sign bit, exponent bits, and a mantissa (also known as significand) bits.

To convert the number -1552.225 into IEEE floating-point format (32 bits), we need to follow these steps:

1. Determine the sign bit: Since the number is negative, the sign bit will be 1.

2. Convert the absolute value of the number into binary form: To do this, we can use the standard method of converting decimal numbers into binary. The absolute value of 1552.225 is 1552.225. So, the binary form of this number will be 11000010000.001.

3. Normalize the binary form: To fit the number into the IEEE floating-point format, we need to normalize it. This means shifting the decimal point to the left until there is only one non-zero digit before the decimal point. In this case, we need to shift the decimal point 10 places to the left, resulting in 1.1000010000001 x 10^3.

4. Determine the exponent bits: The exponent bits represent the power of 2 to which the normalized number is raised. In this case, the number is raised to the power of 3, so the exponent bits will be 3 + 127 = 130 in binary form, which is 10000010.

5. Determine the mantissa bits: The mantissa bits represent the significant digits of the normalized number. In this case, the mantissa bits will be the binary form of 1000010000001, which is 10000100000010000000000.

6. Combine all the bits: The final IEEE floating-point representation of -1552.225 will be 1 10000010 10000100000010000000000. This can be written in hexadecimal form as BF 46 40 00.

Therefore, the IEEE floating-point format (32 bits) for N=-1552.225 is BF 46 40 00.