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Since an int uses 31 bits (+ ~1 bit for the sign), just double 2^30 to get approximately 2 billion. For an unsigned int using 32 bits, double again for 4 billion.
For a given IEEE-754 floating point number X, if 2^E <= abs(X) < 2^(E+1) then the distance from X to the next largest representable floating point number (epsilon) is: epsilon = 2^(E-52) % For a 64-bit float (double precision) epsilon = 2^(E-23) % For a 32-bit float (single precision) epsilon = 2^(E-10) % For a 16-bit float (half precision) The above equations allow us to compute the following ...
The most common 32-bit floating-point format, IEEE-754 binary32, does not have eight bits for the whole number part. It has one bit for a sign, eight bits for an exponent field, and 23 bits for a significand field (a fraction part). The sign bit determines whether the number is positive (0) or negative (1). The exponent field, e, has several uses.
A 32 32 bit integer can be represented as b1b2b3 ⋯b32 b 1 b 2 b 3 ⋯ b 32, where all of these are bits (so they are either 0 0 or 1 1). There are 232 2 32 possibilities for such integers.
The only real difference here is the size. All of the int types here are signed integer values which have varying sizes Int16: 2 bytes Int32 and int: 4 bytes Int64 : 8 bytes There is one small difference between Int64 and the rest. On a 32 bit platform assignments to an Int64 storage location are not guaranteed to be atomic. It is guaranteed for all of the other types.
I saw in MSDN documents that the maximum value of Int32 is 2,147,483,647, hexadecimal 0x7FFFFFFF. I think, if it's Int32 it should store 32-bit integer values that finally should be 4,294,967,295 and hexadecimal 0xFFFFFFFF.
I have a very basic question regarding computers and number representations. I was wondering why it is that 2^31 -1 is the largest positive integer representation for 32-bit binary while 2^31 is the largest negative value?
In an UNSIGNED 32-bit number, the valid values are from 0 to 2³² − 1 (instead of 1 to 2³², but the same number of VALUES, about 4.2 billion). In a SIGNED 32-bit number, one of the 32 bits is used to indicate whether the number is negative or not. This reduces the number of values by a factor of 2¹, or by half.
So there's something I just can't understand about ieee-754. The specific questions are: Which range of numbers can be represented by IEEE-754 standard using base 2 in single (double) precision?
In your case, if the number of bits on IEEE 754 are: 16 Bits you have 1 for the sign, 5 for the exponent and 10 for the mantissa. The largest number represented is 4,293,918,720. 32 Bits you have 1 for the sign, 8 for the exponent and 23 for the mantissa. The largest number represented is 3.402823466E38.