How can I figure out the boolean functions for the output of a 4-bit by 4-bit BCD Adder?

(If I use the truth table and k-maps to solve it, there would be 512 different combinations. This would take ages!)

PS: I need the functions for my Verilog code (data-flow model).

Chapter 4 Combinational Logic Addend Augend Carry K out 4-bit binary adder Z8 Z4 Zz Z, Carry in Output carry 0 4-bit binary adder Sg $4 S, S FIGURE 4.14 Block diagram of a BCD adder