[billpg]

I was surprised to see addition in there.

Hash functions use bit-wise operators. This is a world where "integers" are simply convenient fixed-sized blobs of bits and all bits are equally significant.

Addition is an arithmetic operation. Bits have significance in this world. The state of the input bits have more "influence" over the left hand bits of the result than the right hand bits.

Look at abcd+efgh=ijkl (Ignoring any overflow'd bits per SHA-256.)

To find the value of bit l, you only need to know bits d and h. You need to know all eight input bits to know the value of bit i.