How is RAM able to acess any place in memory at O(1) speed

Question

We are taught that the abstraction of the RAM memory is a long array of bytes. And that for the CPU it takes the same amount of time to access any part of it. What is the device

Answer 1

Let's say your RAM has 2^64 cells (places where it is possible to store a single value, let's say 8-bit). Then it needs 64 pins to address every cell with a different number. When at the input pins of your RAM there 'appears' a binary number X the RAM can send the value from cell addressed X to some output pins, and your CPU can get the value from there. In hardware the addressing can be done quite easily, for example by using multiple NAND gates (such 'addressing device' from some logic gates is called a decoder).

So it is all happening at the hardware-level, this is just direct addressing. If the CPU is able to provide 64 bits to 64 pins of your RAM it can address every single memory cell (as 64 bit is enough to represent any number up to 2^64 -1). The only reason why you do not get the value immediately is a kind of 'propagation time', so time it takes for the signal to go through all the logic gates in the circuit.