First I'm going to assume you already know how binary numbers work because learning how to add or subtract binary numbers doesn't make much sense if you don't know how to count in binary.

I'm also going to assume you have basic klowledge about FILT, know about BRAY annihilation and how to encode and decode signals into BRAY/FILT, as explained in this save (I'm adding it for completeness):

You have to realize that FILT operations like AND, OR and XOR work on all 30 bits/wavelengths of a BRAY simultaniously. For instance in you put a FILT in OR mode and shine a BRAY through it, the BRAY's 1-wavelength will be logically ORed with the 1-wavelength of the FILT's ctype, the BRAY's 2-wavelength will be ORed with the 2-wavelength of the FILT's ctype, etc. up to the 30-wavelength all in one go.

Now we have the basics down we can start building an adder. The simplest way to do this is to build a cascade of half adders with one half adder for every bit/wavelength that has to be processed, IOW if you want to add two 8-bit numbers you'd use 8 half adders and if you want to add two 29-bit numbers you'd use 29 half adders.

A half adder adds two bits/wavelengths together and has two outputs: a sum bit and a carry bit, where the carry bit indicates that the sum bit has overflown and a 1 has to be added to the calculation of the next bit. The calculation of the sum bits and carry bits is straight forward: the sum bit is calculated bt taking the logical XOR of the inputs and the carry bit is calculated by taking the logical AND of the inputs (meaning a sum bit becomes 1 if only one of the input bits is 1 and is 0 otherwise, a carry bit becomes 1 only if both input bits are 1 and is zero otherwise). This is all explained in depth in the wiki link above.

Because we're constructing our half adders in FILT this means we're calculating the sum bits and carry bits for all wavelengths simultaniously as explained above. To make a fully functioning adder we simply use one half adder to calculate the sum bits and the carry bits for all wavelengths, next we'll shift our carry bits to the left so they'll be added to the next larger bits/wavelengths and add the sum bits to the shifted carry bits with the next half adder, we'll repeat this process as many times as there are bits/wavelenths to calculate.

Only dry theory in this first post, I'll create demonstration saves for the half adder and complete adders later. Please ask questions if anything is unclear sofar, I'll adapt my demonstation saves to your questions.

You have 2 values: A and B

A' = A XOR B

B' = (A AND B) << 1

Repeat 29 times for 29-bit addition and take the final value of A as the result