Saturday, May 28, 2022

Registers and RAM: Crash Course Computer Science #6

Hi, I’m Carrie Anne and welcome to CrashCourse Computer Science. So last episode, using just logic gates, webuilt a simple ALU, which performs arithmetic and logic operations, hence the ‘A’ andthe ‘L’. But of course, there’s not much point incalculating a result only to throw it away – it would be useful to store that value somehow, and maybe even run several operations in a row. That's where computer memory comes in! If you've ever been in the middle of a longRPG campaign on your console, or slogging through a difficult level on Minesweeper onyour desktop, and your dog came by, tripped and pulled the power cord out of the wall,you know the agony of losing all your progress. .

Condolences. But the reason for your loss is that yourconsole, your laptop and your computers make use of Random Access Memory, or RAM, whichstores things like game state – as long as the power stays on. Another type of memory, called persistentmemory, can survive without power, and it’s used for different things; We'll talk aboutthe persistence of memory in a later episode. Today, we’re going to start small – literally by building a circuit that can store one.. single.. bit of information. After that, we’ll scale up, and build ourvery own memory module, and we’ll combine .

It with our ALU next time, when we finallybuild our very own CPU! INTRO All of the logic circuits we've discussedso far go in one direction – always flowing forward – like our 8-bit ripple adder fromlast episode. But we can also create circuits that loopback on themselves. Let’s try taking an ordinary OR gate, andfeed the output back into one of its inputs and see what happens. First, let’s set both inputs to 0. So 0 OR 0 is 0, and so this circuit alwaysoutputs 0. .

If we were to flip input A to 1. 1 OR 0 is 1, so now the output of the OR gateis 1. A fraction of a second later, that loops backaround into input B, so the OR gate sees that both of its inputs are now 1. 1 OR 1 is still 1, so there is no change inoutput. If we flip input A back to 0, the OR gatestill outputs 1. So now we've got a circuit that records a“1” for us. Except, we've got a teensy tiny problem – thischange is permanent! No matter how hard we try, there’s no wayto get this circuit to flip back from a 1 .

To a 0. Now let’s look at this same circuit, butwith an AND gate instead. We'll start inputs A and B both at 1. 1 AND 1 outputs 1 forever. But, if we then flip input A to 0, becauseit’s an AND gate, the output will go to 0. So this circuit records a 0, the oppositeof our other circuit. Like before, no matter what input we applyto input A afterwards, the circuit will always output 0. Now we’ve got circuits that can record both0s and 1s. The key to making this a useful piece of memoryis to combine our two circuits into what is .

Called the AND-OR Latch. It has two inputs, a “set” input, which setsthe output to a 1, and a “reset” input, which resets the output to a 0. If set and reset are both 0, the circuit justoutputs whatever was last put in it. In other words, it remembers a single bitof information! Memory! This is called a “latch” because it “latchesonto” a particular value and stays that way. The action of putting data into memory iscalled writing, whereas getting the data out is called reading. .

Ok, so we’ve got a way to store a singlebit of information! Great! Unfortunately, having two different wiresfor input – set and reset – is a bit confusing. To make this a little easier to use, we reallywant a single wire to input data, that we can set to either 0 or 1 to store the value. Additionally, we are going to need a wirethat enables the memory to be either available for writing or “locked” down –which iscalled the write enable line. By adding a few extra logic gates, we canbuild this circuit, which is called a Gated Latch since the “gate” can be opened orclosed. .

Now this circuit is starting to get a littlecomplicated. We don’t want to have to deal with all theindividual logic gates… so as before, we’re going to bump up a level of abstraction, andput our whole Gated Latch circuit in a box — a box that stores one bit. Let’s test out our new component! Let’s start everything at 0. If we toggle the Data wire from 0 to 1 or1 to 0, nothing happens – the output stays at 0. That’s because the write enable wire isoff, which prevents any change to the memory. So we need to “open” the “gate” byturning the write enable wire to 1. .

Now we can put a 1 on the data line to savethe value 1 to our latch. Notice how the output is now 1. Success! We can turn off the enable line and the outputstays as 1. Once again, we can toggle the value on thedata line all we want, but the output will stay the same. The value is saved in memory. Now let’s turn the enable line on againuse our data line to set the latch to 0. Done. .

Enable line off, and the output is 0. And it works! Now, of course, computer memory that onlystores one bit of information isn’t very useful — definitely not enough to run Frogger. Or anything, really. But we’re not limited to using only onelatch. If we put 8 latches side-by-side, we can store8 bits of information like an 8-bit number. A group of latches operating like this iscalled a register, which holds a single number, and the number of bits in a register is calledits width. .

Early computers had 8-bit registers, then16, 32, and today, many computers have registers that are 64-bits wide. To write to our register, we first have toenable all of the latches. We can do this with a single wire that connects to all of their enable inputs, which we set to 1. We then send our data in using the 8 datawires, and then set enable back to 0, and the 8 bit value is now saved in memory. Putting latches side-by-side works ok fora small-ish number of bits. A 64-bit register would need 64 wires runningto the data pins, and 64 wires running to the outputs. .

Luckily we only need 1 wire to enable allthe latches, but that’s still 129 wires. For 256 bits, we end up with 513 wires! The solution is a matrix! In this matrix, we don’t arrange our latchesin a row, we put them in a grid. For 256 bits, we need a 16 by 16 grid of latcheswith 16 rows and columns of wires. To activate any one latch, we must turn onthe corresponding row AND column wire. Let’s zoom in and see how this works. We only want the latch at the intersectionof the two active wires to be enabled, but all of the other latches should stay disabled. .

For this, we can use our trusty AND gate! The AND gate will output a 1 only if the rowand the column wires are both 1. So we can use this signal to uniquely selecta single latch. This row/column setup connects all our latcheswith a single, shared, write enable wire. In order for a latch to become write enabled,the row wire, the column wire, and the write enable wire must all be 1. That should only ever be true for one singlelatch at any given time. This means we can use a single, shared wirefor data. Because only one latch will ever be writeenabled, only one will ever save the data .

— the rest of the latches will simply ignorevalues on the data wire because they are not write enabled. We can use the same trick with a read enablewire to read the data later, to get the data out of one specific latch. This means in total, for 256 bits of memory,we only need 35 wires – 1 data wire, 1 write enable wire, 1 read enable wire, and 16 rowsand columns for the selection. That’s significant wire savings! But we need a way to uniquely specify eachintersection. We can think of this like a city, where youmight want to meet someone at 12th avenue .

And 8th street — that's an address that definesan intersection. The latch we just saved our one bit into hasan address of row 12 and column 8. Since there is a maximum of 16 rows, we store the row address in a 4 bit number. 12 is 1100 in binary. We can do the same for the column address: 8 is 1000 in binary. So the address for the particular latch wejust used can be written as 11001000. To convert from an address into somethingthat selects the right row or column, we need a special component called a multiplexer — whichis the computer component with a pretty cool name at least compared to the ALU. .

Multiplexers come in all different sizes,but because we have 16 rows, we need a 1 to 16 multiplexer. It works like this. You feed it a 4 bit number, and it connectsthe input line to a corresponding output line. So if we pass in 0000, it will select thevery first column for us. If we pass in 0001, the next column is selected,and so on. We need one multiplexer to handle our rowsand another multiplexer to handle the columns. Ok, it’s starting to get complicated again,so let’s make our 256-bit memory its own component. Once again a new level of abstraction! .

It takes an 8-bit address for input – the4 bits for the column and 4 for the row. We also need write and read enable wires. And finally, we need just one data wire, whichcan be used to read or write data. Unfortunately, even 256-bits of memory isn’tenough to run much of anything, so we need to scale up even more! We’re going to put them in a row. Just like with the registers. We’ll make a row of 8 of them, so we canstore an 8 bit number – also known as a byte. To do this, we feed the exact same addressinto all 8 of our 256-bit memory components .

At the same time, and each one saves one bitof the number. That means the component we just made canstore 256 bytes at 256 different addresses. Again, to keep things simple, we want to leavebehind this inner complexity. Instead of thinking of this as a series ofindividual memory modules and circuits, we’ll think of it as a uniform bank of addressablememory. We have 256 addresses, and at each address,we can read or write an 8-bit value. We’re going to use this memory componentnext episode when we build our CPU. The way that modern computers scale to megabytesand gigabytes of memory is by doing the same thing we’ve been doing here — keep packagingup little bundles of memory into larger, and .

Larger, and larger arrangements. As the number of memory locations grow, ouraddresses have to grow as well. 8 bits hold enough numbers to provide addresses for 256 bytes of our memory, but that’s all. To address a gigabyte – or a billion bytesof memory – we need 32-bit addresses. An important property of this memory is thatwe can access any memory location, at any time, and in a random order. For this reason, it’s called Random-AccessMemory or RAM. When you hear people talking about how much RAM a computer has – that's the computer’s memory. RAM is like a human’s short term or workingmemory, where you keep track of things going .

On right now – like whether or not you hadlunch or paid your phone bill. Here’s an actual stick of RAM – with 8 memorymodules soldered onto the board. If we carefully opened up one of these modulesand zoomed in, The first thing you would see are 32 squares of memory. Zoom into one of those squares, and we cansee each one is comprised of 4 smaller blocks. If we zoom in again, we get down to the matrixof individual bits. This is a matrix of 128 by 64 bits. That’s 8192 bits in total. Each of our 32 squares has 4 matrices, sothat’s 32 thousand, 7 hundred and 68 bits. .

And there are 32 squares in total. So all in all, that’s roughly 1 millionbits of memory in each chip. Our RAM stick has 8 of these chips, so intotal, this RAM can store 8 millions bits, otherwise known as 1 megabyte. That’s not a lot of memory these days — thisis a RAM module from the 1980’s. Today you can buy RAM that has a gigabyteor more of memory – that’s billions of bytes of memory. So, today, we built a piece of SRAM – StaticRandom-Access Memory – which uses latches. There are other types of RAM, such as DRAM, Flash memory, and NVRAM. .

These are very similar in function to SRAM,but use different circuits to store the individual bits — for example, using different logicgates, capacitors, charge traps, or memristors. But fundamentally, all of these technologiesstore bits of information in massively nested matrices of memory cells. Like many things in computing, the fundamentaloperation is relatively simple.. it’s the layers and layers of abstraction that’smind blowing — like a russian doll that keeps getting smaller and smaller and smaller. I’ll see you next week. Credits .


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