Yes. The sign bit of 32-bit integers and of 32-bit floats is set (to one) when the value is negative and clear (to zero) when the value is positive or zero.

The mantissa represents a number in 24-bit base two positional notation that looks like this:

1.xxxxxxxxxxxxxxxxxxxxxxx (x = 0 or 1; there are 23 x's)

**Very tricky:**
The mantissa represents the 23-bit binary fraction part
of a 24-bit number that starts with a "1".
The 2^{0} place (the one's place) is presumed
to contain a 1 and *is not present in the mantissa.*
This trick gives us 24 bits of precision with only 23 bits.

For example, the binary number `1.11110000101101101010001`

is represented as `11110000101101101010001`

If you had a daughter would you name her Mantissa?