title: Floating-point: "The leading 1 is 'implicit' in the significand." -- ...huh?
body: <p>I'm learning about the representation of floating-point IEEE 754 numbers, and my textbook says:</p>
  
  <blockquote>
    <p>To pack even more bits into the significand, IEEE 754 makes the leading 1-bit of normalized binary numbers implicit. Hence, the number is actually 24 bits long in single precision (implied 1 and 23-bit fraction), and 53 bits long in double precision (1 + 52).</p>
  </blockquote>
  
  <p>I don't get what "implicit" means here... what's the difference between an explicit bit and an implicit bit? Don't all numbers have the bit, regardless of their sign?</p>