“Also, how can a truly one-bit digital operation be irreversible? The only such operations that both input and output one bit are the identity and inversion gates, both of which are reversible.”
Setting or clearing a bit register regardless of what was there before is a one-bit irreversible operation (the other two one-bit input, one-bit output functions are constant 1 and constant 0).
Nitpick nitpick:
“Also, how can a truly one-bit digital operation be irreversible? The only such operations that both input and output one bit are the identity and inversion gates, both of which are reversible.”
Setting or clearing a bit register regardless of what was there before is a one-bit irreversible operation (the other two one-bit input, one-bit output functions are constant 1 and constant 0).