An example of a 1-bit architecture that was actually marketed as a CPU is the Motorola MC14500B Industrial Control Unit. There are also several design studies for 1-bit architectures in academia, and corresponding 1-bit logic can also be found in programming.
A typical sequence of instructions from a program for a 1-bit architecture might be:
load digital input 1 into a 1-bit register;
OR the value in the 1-bit register with input 2, leaving the result in the register;
write the value in the 1-bit register to output 1.
1-bit CPUs can be considered obsolete now, not many kinds have been produced (MC14500B and WDR-1 known) and none known to be available in any computer component store (except, as of 2014[update], a few on Ebay).