Odd Parity Output as Input to Second Circuit
As far as I know, the first circuit is basically 2 cascaded XOR gates which outputs 1 if the the no of high inputs are odd. Hence circuit 1 outputs 1 when odd parity is satisfied. If you want circuit two to be a circuit whose output is zero when odd parity is satisfied then just add a not gate to the output of circuit 1. 







simulate this circuit &ndash; Schematic created using CircuitLab

Is this what you are looking for?
 I bet you can simplify circuit 2 by using boolean algebra when u go for AND-OR-INVERT implementation.