I'm designing a 8421 BCD to 84-2-1 BCD converter circuit. The truth table is:
Decimal | ABCD | WXYZ 0 | 0000 | 0000 1 | 0001 | 0111 2 | 0010 | 0100 . . . . . . 9 | 1001 | 1111
Everything after decimal 9 is a don't care. I started by creating Karnaugh maps for each
W, X, Y, Z. From the Karnaugh maps, I found the following equations:
W = (A)(~B)(~C) + (~A)(B)(C+D) X = (~A)(~C)(~D) + (~A)(~B) + (~B)(D) Y = (~C)(D)([~A]+[~B]) + (~A)(C)(~D) Z = (D)([~A]+[~B][~C])
Where multiplication means AND, addition means OR, and ~ means NOT. I'm unsure of how draw a circuit with the appropriate logic gates from here. Do I create a circuit for each letter and then AND all of the outputs together? Do I combine all of the expressions (as in W+X+Y+Z or WXYZ) and simplify the expressions from there, then create a circuit using the new simplified expression? I'm not really interested in what this particular circuit will actually look like, I'm trying to find tackle the more general concept of moving from truth tables to circuit schematics.