How would this digital logic problem be solved?

A switching circuit has three inputs and two outputs. The output variables, a and b, represent the first and second bits, respectively, of a binary number, N.N equals the number of inputs which are 0. For example, if x=1, y=0, z=1, then a=0, b=1. Write sum of products expansion for a and b.|||xyz ab


000 11


001 10


010 10


011 01


100 10


101 01


110 01


111 00





a = 000+001+010+100 = x'y'+x'z'+y'z'


b = 000+011+101+110 = x'y'z'+z'yz+zy'z+xyz' = exor of xyz