# Help Identifying a Gate In Nielsen and Chuang I am seeking help to identify the oracle gates listed in this example. I understand that the right-most one is a toffoli gate, but what are the other ones? Specifically, I do not understand what a black versus white circle means for gate representation. This example comes from Nielsen and Chuang page 256

Here are the corresponding decompositions of each gate with use of Toffoli and $$X$$ gates: The first one applies $$X$$ gate on the third qubit if control qubits are in the $$|00\rangle$$ state. The second one applies $$X$$ gate on the third qubit if control qubits are in the $$|01\rangle$$ state. The third one applies $$X$$ gate on the third qubit if control qubits are in the $$|10\rangle$$ state. The fourth one is the Toffoli gate that applies $$X$$ gate if control qubits are in the $$|11\rangle$$ state. In all other cases, they do nothing. The black (white) circle means that the corresponding qubit should be $$|1\rangle$$ $$(|0\rangle)$$ to satisfy the condition of the gate. Multiple circles are for multiple conditions on the control qubits.