How much memory did Apollo 11 have?

The Apollo Guidance Computer's (AGC) program memory was hardware in the literal sense. In core-rope memory, wires were threaded through or around tiny ferrite rings; each wire passing through a core represented a one, and each one bypassing it represented a zero. These "ropes" were woven by hand over months, and were then unchangeable. That fixed portion held 36,864 words, compared with the 2,048 words of erasable core memory the computer actually worked with; each word had 16 bits, one of them for error checking.

Working memory stored state vectors, orientations, intermediate results, and the numbers the crew entered via the DSKY keyboard using verb and noun codes. Since there was barely any margin left, a small real-time operating system prioritized tasks and dropped the ones that didn't fit. That is exactly what happened during Apollo 11's descent: the 1201 and 1202 alarms indicated the computer was overloaded and restarting tasks. Even so, the lunar module landed, because the software was designed for exactly that case.

By today's standards, that's nothing: a single smartphone photo takes up many times more. But the comparison is misleading, because that computer didn't have to support an operating system, graphics, or applications — only navigation, control, and display: fixed-scope embedded tasks. Calculations were done with integers and carefully chosen scaling, measurements came from the inertial platform and the sextant, and the crew made the call when in doubt. There was also additional computing power available at Mission Control in Houston, which relayed orbital data by radio.