Addressing Memory (Pt1) - Computerphile

Key Takeaways

so in our previous video on how memory worked we got to the point from storing one bit of information that we could set or reset it to the flip-flop where we could store a bit of information and then we arranged four of them together in parallel so we could store four bits of information so what we did we had four inputs DN to D3 which gave us our input and four outputs Q to Q3 which gave us our output and we connected for each of the flip-flops the clock input together so that when we strob this input it stored all the information on the data inputs and presented it out at the output this has still only allowed us to store one piece of information it was a bigger piece we could store here a number between not and 15 or if we use two's complement between minus 8 and 7 but it was still only one piece of information so we're going to look at now is how we can arrange flip-flops so we can store more than one piece of information so actually if you're implementing a membership like this one which which is a 8K by 8bit memory chip you wouldn't use flipflops as we've seen them before you'd actually arrange about six transistors to store each bit just so that you can fit more onto the actual silicon if you put flipflops as we design them on they take up more space also we're not going to consider like this is an 8 bit wide bit of memory or bite wide memory we'll still consider one bit so we're only going to store one bit of information but we're going to store multiple different bits if you did want to store eight bits of information you could just have eight chips one for each bit that you wanted to store so I'm just going to use the flip-flop symbol that we had before to represent it so we' got our data input which we'll call D we' got our output Q we've also got the inverted Q output and we have our clock input as well that we can use to tell it to store it so whatever is on the input is stored in the flip problem goes to the output when we take this low and then take it high again or vice versa depending on how it's actually built now we want to store more than one bit of information so what I'm going to do is I'm going to store two bits of information so I have another flip-flop exactly the same so now we have two bits of information now there's several things we need to do we want to have one input to our system so we have one data bit that we're going to store and we want to be able to choose whether we store it in this flip-flop or in that flipflop well the first thing we need is some way of saying which flipflops value we're actually interested in storing the CPU refers to every single memory location by a unique identifier but rather than having a name like we get in the programming language the computer uses a binary number to refer to each memory location this is what we would call the address so in this case I'm going to say this is at address zero and this one is at address one so now I want to be able to access either this one or this one well first thing I'm going to do is I'm going to have a data input which I'm going to call D in here and that's where we're going to put our signal now if we think about how flip-flop Works they only change the value they store when we strobe the clock input so actually we can connect the input directly to the input of the first flip-flop and we can also connect it directly to the input of the second flip-flop like so so how do we choose which one we want to St in well we could have in this case two strobe lines and just strobe the right one well that would work fine for two bits and it wouldn't be too bad if we had four flip-flops but if you think about it if you've got 64 kilobits of memory that's 65,536 different wires and so it gets unmanageable when you get to high numbers so what we do is we say well actually we're going to have an input which we'll call a in the address input and if this is zero then we're going to refer to this one and if this contains one we're going to refer to this one we'll also have a signal W which we'll use to say we want to write whatever bit is in D in to whichever flip-flop is specified by a in so what we want to do is to be able to strobe the input to the zero flip-flops clock pin when a in contains zero and W is strobed or strobe the input on one flip-flop when a in contains one and W is strob so we need to connect via digital logic again these inputs to the clock input of flip zero or the clock input of flip-flop one and to do that we use our old friend the and gate again going to start with flip-flop one because it's the simpler one to think about how we do this we want this clock input to be strobed when w is strobed and a in contains a one and so the easiest way to do that if remember our and Gates and you can look back at some of the videos on number file if you forgotten about them up here this is a and gate so if we put an and gate in here we draw that like so now if we think about an and gate again it's got two inputs A and B and an output which again we'll use Q so if we look here we see that whenever a is one the output matches B so when a is one and B is zero the output is zero when a is one and B is one the output is one so we can use this fact of these values here in our circuit here we want clock to be whatever the value of w is which we've connected to input B on the hand gate whenever the input a in is one so we can just connect that line directly in like that and so now whenever we strobe W the clock input on flip-flop one will only be strobed if a in contains one or the address one now how do we do the same for flip-flop zero well we want the same thing to happen so I should bring my wires down here so so what we need to do now is work out what are going to be the right inputs for A and B on this handgate now the input for B is easy because it's exactly the same as this one here the W signal the right signal the same we want to write it we just bring this down and connect it up but we need this thing to be one whenever a in is zero so the way we do that again remembering in digital logic is that we use a simple notot gate like this which just inverts it so when the input to the not gate is zero the output is one when the input to the not gate is one the output is zero so we can connect this in like so and so now what we've got said up is that we've got three inputs W it says when we want to write something to our flipflops D in which contains the value we want to write and a in which tells us whether we want to write to flipflop zero or flip-flop one depending on the value of zero or one in a in we either store the value in that one or we store it in that one and of course you can expand this up to complicated draid but if you wanted to store say four you'd have two a inputs so you have a Zer which would contain Bit Zero of your binary input and you'd have a one which would contain bit one of course remember your binary inputs will then be A1 and a z and so you'd be able to refer to 0 0 which will give you location 0 again 01 which will give you address one 1 0 which would give you address two and one one which would give you address three and all we need to do is build up a more complicated circuit which combined a z and A1 or not a z and not A1 with the w signal to connect to each of these flip flops so that's how we would do the writing to one we can choose whichever FL flop we want by the address and then we can strobe the W thing to write into that one or that one but what about reading how do we combine the two outputs from our flip-flops into a single the arm system in the first Archimedes would run reliably well above 100° C said way this is just the half adder we want a binary full adder