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  2. 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.

  3. 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 ...

  4. 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.

  5. How is the max number for a $32$-bit integer calculated?

    math.stackexchange.com/questions/2640747

    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.

  6. 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.

  7. 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.

  8. 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?

  9. Why has the Int32 type a maximum value of 2³¹ − 1?

    stackoverflow.com/questions/3826704

    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.

  10. The upper and lower limits of IEEE-754 standard

    math.stackexchange.com/questions/2607697/the-upper-and-lower-limits-of-ieee...

    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?

  11. max float represented in IEEE 754 - Stack Overflow

    stackoverflow.com/questions/10233444

    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.