Fixed point vs Floating point number

Question

I just can t understand fixed point and floating point numbers due to hard to read definitions about them all over Google  But none that I have read provide a simple enough explanation of what they really are  Can I get a plain definition with example

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Take the number 123 456789     As an integer  this number would be 123  As a fixed point  2   this number would be 123 46  Assuming you rounded it up   As a floating point  this number would be 123 456789   Floating point lets you represent most every number with a great deal of precision   Fixed is less precise  but simpler for the computer

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A fixed point number has a specific number of bits  or digits  reserved for the integer part  the part to the left of the decimal point  and a specific number of bits reserved for the fractional part  the part to the right of the decimal point   No matter how large or small your number is  it will always use the same number of bits for each portion  For example  if your fixed point format was in decimal IIIII FFFFF then the largest number you could represent would be 99999 99999 and the smallest non-zero number would be 00000 00001  Every bit of code that processes such numbers has to have built-in knowledge of where the decimal point is   A floating point number does not reserve a specific number of bits for the integer part or the fractional part  Instead it reserves a certain number of bits for the number  called the mantissa or significand  and a certain number of bits to say where within that number the decimal place sits  called the exponent   So a floating point number that took up 10 digits with 2 digits reserved for the exponent might represent a largest value of 9 9999999e 50 and a smallest non-zero value of 0 0000001e-49

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The term    fixed point    refers to the corresponding manner in which numbers are represented  with a fixed number of digits after  and sometimes before  the decimal point   With floating-point representation  the placement of the decimal point can    float    relative to the significant digits of the number   For example  a fixed-point representation with a uniform decimal point placement convention can represent the numbers 123 45  1234 56  12345 67  etc  whereas a floating-point representation could in addition represent 1 234567  123456 7  0 00001234567  1234567000000000  etc

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From my understanding  fixed-point arithmetic is done using integers  where the decimal part is stored in a fixed amount of bits  or the number is multiplied by how many digits of decimal precision is needed   For example  If the number 12 34 needs to be stored and we only need two digits of precision after the decimal point  the number is multiplied by 100 to get 1234  When performing math on this number  we d use this rule set  Adding 5620 or 56 20 to this number would yield 6854 in data or 68 54   If we want to calculate the decimal part of a fixed-point number  we use the modulo     operand   12 34  pseudocode    v1   1234   100    get the whole number v2   1234   100    get the decimal number  100ths of a whole   print v1         v2     12 34    Floating point numbers are a completely different story in programming  The current standard for floating point numbers use something like 23 bits for the data of the number  8 bits for the exponent  and 1 but for sign  See this Wikipedia link for more information on this

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A fixed point number just means that there are a fixed number of digits after the decimal point   A floating point number allows for a varying number of digits after the decimal point   For example  if you have a way of storing numbers that requires exactly four digits after the decimal point  then it is fixed point   Without that restriction it is floating point   Often  when fixed point is used  the programmer actually uses an integer and then makes the assumption that some of the digits are beyond the decimal point   For example  I might want to keep two digits of precision  so a value of 100 means actually means 1 00  101 means 1 01  12345 means 123 45  etc   Floating point numbers are more general purpose because they can represent very small or very large numbers in the same way  but there is a small penalty in having to have extra storage for where the decimal place goes

[numbers] Fixed point vs Floating point number

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