How to work out if an IEEE 754 floating point number is normalized?
For single-precision floating-point numbers you need to check if the following condition holds for the exponent $e$: $0 &lt; e &lt; 255$. The exponent occupies bits $30 .. 23$ (including both ends) of a floating-point number.

For double-precision floating-point numbers you need to check if $0 &lt; e &lt; 2047$. The exponent occupies bits $62 .. 52$ in this case.

Essentially, for IEEE 754 floating-point numbers one has to check that the bits of the exponent are not all 1's and not all 0's. All zero bits correspond either to subnormal numbers or to signed zero. And when all bits of the exponent are ones it corresponds to $+\infty, -\infty$ or NaN (not a number).