What is the difference between the float and integer data type when the size is the same

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What the difference between the float and integer data type when size is same

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Floats are used to store a wider range of number than can be fit in an integer  These include decimal numbers and scientific notation style numbers that can be bigger values than can fit in 32 bits  Here s the deep dive into them  http   en wikipedia org wiki Floating point

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float stores floating-point values  that is  values that have potential decimal places int only stores integral values  that is  whole numbers   So while both are 32 bits wide  their use  and representation  is quite different  You cannot store 3 141 in an integer  but you can in a float   Dissecting them both a little further   In an integer  all bits are used to store the number value  This is  in Java and many computers too  done in the so-called two s complement  This basically means that you can represent the values of  minus 231 to 231 nbsp  minus  nbsp 1   In a float  those 32 bits are divided between three distinct parts  The sign bit  the exponent and the mantissa  They are laid out as follows   S EEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM   There is a single bit that determines whether the number is negative or non-negative  zero is neither positive nor negative  but has the sign bit set to zero   Then there are eight bits of an exponent and 23 bits of mantissa  To get a useful number from that   roughly  the following calculation is performed      M    2E    There is more to it  but this should suffice for the purpose of this discussion   The mantissa is in essence not much more than a 24-bit integer number  This gets multiplied by 2 to the power of the exponent part  which  roughly  is a number between  minus 128 and 127   Therefore you can accurately represent all numbers that would fit in a 24-bit integer but the numeric range is also much greater as larger exponents allow for larger values  For example  the maximum value for a float is around 3 4    1038 whereas int only allows values up to 2 1    109   But that also means  since 32 bits only have 4 2    109 different states  which are all used to represent the values int can store   that at the larger end of float s numeric range the numbers are spaced wider apart  since there cannot be more unique float numbers than there are unique int numbers   You cannot represent some numbers exactly  then  For example  the number 2    1012 has a representation in float of 1 999 999 991 808  That might be close to 2 000 000 000 000 but it s not exact  Likewise  adding 1 to that number does not change it because 1 is too small to make a difference in the larger scales float is using there   Similarly  you can also represent very small numbers  between 0 and 1  in a float but regardless of whether the numbers are very large or very small  float only has a precision of around 6 or 7 decimal digits  If you have large numbers those digits are at the start of the number  e g  4 51534    1035  which is nothing more than 451534 follows by 30 zeroes     and float cannot tell anything useful about whether those 30 digits are actually zeroes or something else   for very small numbers  e g  3 14159    10 minus 27  they are at the far end of the number  way beyond the starting digits of 0 0000

[java] What is the difference between the float and integer data type when the size is the same?

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