4.1 The representation

The representation of a number using the floating point method has three components:

• The mantissa.is a number n ∈ [1…2), which means it is at least 1, and less than 2.
  • Note that the first part of a mantissa is implied. In other words, the 1. portion is implied. This means a mantissa 1.01101₂ is represented as the bit pattern 01101₂.
• The sign s indicates whether a number is negative or not. It is conventional to use a value of 1 to indicate a negative value, and 0 to indicate a non-negative value.
• The exponent x specifies the magnitude 2^x−b, where b is an offset. so that x can be an unsigned number.

The value represented by such a floating number is, then, s = 0 ⇒ v = n2^x−b,s = 1 ⇒ v = −n2^x−b. Of course, we immediately have a problem: how do we represent 0? Let’s defer this topic for now.