Real numbers are number like:

Whole numbers eg 1, 2 ,3 4 etc

Rational Numbers eg 3/4

Real numbers are also known as floating point numbers.

The real number is stored as 2 seprate bits of data. A storage location called the mantissa holds the complete number without the point.

The exponent holds the number of places that the point must be moved in the orginal number to place it at the left hand side.

For example, what is the exponent of 10110.110

The exponent is 5 because the point has to be moved 5 times to the left hand side. Then you write the number again, this time you rewrite the number without the point, then you write times 2(since it’s binary) and then 0101 since thuis is 5 in binary.

If the number only had 6 bits eg 11.10.11 then you would add two zero’s so that theirs 8 bits.

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Excellent post Ryan, really impressive and the use of the example is great. One minor issue – you say that “real numbers are also known as floating boat numbers”. I think you mean “floating point numbers”