Floating-point: “The leading 1 is 'implicit' in the significand.” — …huh?

Question

I\'m learning about the representation of floating-point IEEE 754 numbers, and my textbook says:

To pack even more bits into the significand, IEEE 754

Answer 1

Here is what they are saying. The first non-zero bit is always going to be 1. So there is no need for the binary representation to include that bit, since you know what it is. So they don't. They tell you where that first 1 is, and then they give the bits after it. So there is a 1 that is not explicitly in the binary representation, whose location is implicit from the fact that they told you where it was.