originally posted byt.man
how can one go about in representing the following Boolean function using NAND gates with a minimum number of gates?
z = A' BC + AB'C + ABC' + ABC
Typically logic designers use K-map but in this particular case the boolean laws can be easily used.
z= A' BC + AB'C + AB
z= A' BC +A(B'C+B)
z=A'BC+A(B+C)
z=A'BC+AB+AC
z=B(A'C+A)+AC
z=AB+BC+AC
As you can see this is just a minimal expression in Sum of Products form.
Since "AND-OR" combination is equivalent to "NAND-NAND" combination, you can relaise the above expression by three 2 input nanad gate and one three input nand gate.