The author says that every real number x can be represented as

x = m * 2^p

where m is an integer(mantissa) and p is an integer (point position)

Well this is clearly wrong, take x = 1/3 for example

1/3 = m * 2^p

m = 1 / (3 * 2^p), where m is an integer, doesn't hold true for any integer p.

If the author had read first 2 pages of

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.h...

they could have avoided the embarrassment.