Binary floating-point numbers are scientific notation except the pieces are all in binary. In proper scientific notation, the only time the digit before the dec

Binary floating-point numbers are scientific notation except the pieces are all in binary. In proper scientific notation, the only time the digit before the decimal point can be 0 is when the number itself is 0. Since the only other digit in binary notation is 1, there is no need to store the digit before the decimal point, since it's always 1... except now you can't store 0. This problem is fixed by reserving one of the exponents for the representation of 0. Some of the formats (e.g. VAX floating point) that introduced this implicit-1-bit for the binary format said that every number with this special-0-exponent was a zero. But IEEE 754 introduced the concept of gradual underflow, and says instead that it is a bit string with the implicit digit before the decimal point as a 0 instead of 1. Putting it differently and more succinctly: a subnormal number is a number that has fewer digits of precision than is normally implied by the format. Which numbers are subnormal numbers is entirely dependent on the floating-point format.