There are two main paths in the floating point adder: exponent calculation and significand calculation. Those paths exchange information to generate the final calculated result. When the significand is scaled, the exponent is adjusted accordingly. The main sub-function includes the significand calculation, which are alignment, fixed-point addition, normalization, and rounding. Normalization is a large percentage of the logic that makes up a floating point adder, and if eliminated, it would give margin to hardware optimization. The lack of normalization, however, may cause some loss of significand bits during operations, something that must be considered. Internal values of the significand are represented in the fixed-point, and they are tightly connected with exponent value in the exponent calculation channel. To implement sub-functions, there needs to be a way to carry exponent and fixed-point significand together as it's done in the standard floating-point system, but with fewer constraints and special cases.
In a sequence of floating point additions, the normalization and rounding steps account for a significant portion of the critical path. When creating compound operations, it is usually recommended to leave normalization and rounding to the final stage of a series of operations. This is because direct access to the internal fixed-point values of a floating-point operation, without normalization or rounding, reduces complexity, area, and critical path and it gives designers control over internal precision. A simple example of a two-stage adder is shown in Figure 4.
By eliminating normalization and rounding, the numerical behavior changes. First, the exponent calculation is somewhat simplified in the first FP adder. Second, the representation of our floating-point output does not comply with the IEEE 754 standard anymore. Third, the second floating-point adder in the chain needs to understand this new representation and it needs to have some information about what happened in the previous calculation to make decisions.