boolean algebra deals with verification of statements and since binary deals with two states, this science was analogous to computer circuits and as such is used here also(edited)

if you do some research on boolean algebra you’d come up with not so pretty symbols used for what we just learnt about AND NOT and OR

. exclusive or or XOR holds a special place in this branch (normal OR is called inclusive or)

XOR addition follows the XOR truth table as defined above

i.e. as we saw just with + rem same as xor gate

1 xorAdd 1 = 0

1 xorAdd 0 = 1

0 xorAdd 1 = 1

0 xorAdd 0 = 0

it’s symbol is

 

hence we can do xor additions

100110

101101 xorAdd

———-

001011

remember no carry as just xor table

another name for xor addition is parity addition

it is to be noted that parity addition is used in cryptography

you have a binary string

a binary key

parity addition them you get your string

it is also useful for checks etc