A BUT gate takes two pairs of input wires (A1, A2 and B1, B2, ) and produces two outputs Y1 and Y2. Output Y1 is 1 when both A1 and B1 are 1, but either A2 or B2 is 0. More precisely:

Y1 = A1 B1 A2' B2' + A1 B1 A2 B2' + A1 B1 A2' B2 

Output Y2 is symmetric: it is 1 when both A2 and B2 are 1, but either A1 or B1 is 0.

a)Draw the truth table for this circuit

b)Draw the logic diagram for a circuit implementing this function that uses 2-input NOR gates only. Hint: First try using some of the boolean identities to simplify the boolean equations.