In Quantum Computation with the simplest maths possible there is a section titled "Doing maths with a controlled-half NOT" which covers a reversible-(N)AND circuit with controlled-half NOTs.
What would the unitary matrix for a controlled-half NOT be?
How could a reversible-XNOR gate be constructed with controlled-half NOTs?
How would a half-adders, full adders & ripple carry adders be constructed from controlled-half NOTs?