Text: Discrete math, computation
Circuits
Problem 7. Give a circuit that solves the problem described by the function f : {T,F}^2 -> {T,F} with f(x1x2) = T if and only if x1 = x2.
Problem 8. Give a circuit that solves the problem described by the function f : {T,F}^3 -> {T,F} with f(x1x2x3) = T if and only if at least one of x1, x2, x3 is F.
Problem 9. Give a circuit that solves the problem described by the function f : {T,F}^4 -> {T,F} with f(x1x2x3x4) = F if and only if x1 = x2 = x3 = x4. (Hint: compare to -(x1Xx2Xx3Ax4)Ax1Vx2Vx3Vx4).
Problem 10. Define the NOR gate to be the gate with inputs x1, x2 and output -(x1Vx2). Prove that NOR is a universal gate.
