• ^ = AND
• v = OR
• ¬ = NOT
• # = XOR

some extra info

• half-adder(a,b) :> (sum,carry) => {a#b,a^b}
• full-adder(a,b,c) :> (sum,carry) => {(a#b)#c,(a^b)v(c^(a#b))}

a5,a4,a3,a2,a1

b5,b4,b3,b2,b1

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s5,s4,s3,s2,s1

X#Y = ¬(A^B)^(AvB)

s1 = a1#b1

s2 = (a2#b2)#(a1^b1)

s3 = (a3#b3)#((a2^b2)v((a2#b2)^(a1^b1)))

s4 = (a4#b4)#((a3^b3)v((a3#b3)^(a2^b2))v((a3#b3)^(a2#b2)^(a1^b1)))

s5 = (a5#b5)#((a4^b4)v((a4#b4)^(a3^b3))v((a4#b4)^(a3#b3)^(a2^b2))v((a4#b4)^(a3#b3)^(a2#b2)^(a1^b1)))