You should look into how a half adder circuit works, basically the circuit calculates the sum of two bits and indicates if there was an overflow (wether the sum doesn't fit into a single bit) called a carry. Calculating the bit sums and bit carries are just simple logical operations (XOR for the sums and AND for the carries) so half adders are relatively easy to build using FILT and BRAY. What complicates things a bit is BRAY annihilation which forces you to set the 30th bit of all input and output values.

Building a simple adder means putting as many half adders in series as you need bits to calculate, you just shift the carry bits to the left one bit so they'll be added to the next larger bit of the bit sum by the next half adder.

This save consists of 29 half adders in series