Code_ The Hidden Language of Computer Hardware and Software - Charles Petzold [73]
One problem with this circuit is that we have no way of stopping it! At some point, the lightbulbs will stop flashing because all the rest of the numbers in the RAM array will be 00h. At that time, you can read the binary sum. But when the counter eventually reaches FFFFh, it will roll over (just like a car odometer) to 0000h and this automated adder will begin adding the numbers again to the sum that was already calculated.
This adding machine has other problems as well. All it does is add, and all it adds are 8-bit numbers. Not only is each number in the RAM array limited to 255, but the sum is limited to 255 as well. The adder also has no way to subtract numbers, although it's possible that you're using negative numbers in two's complements, in which case this machine is limited to handling numbers from -128 through 127. One obvious way to make it add larger numbers (for example, 16-bit values) is to double the width of the RAM array, the adder, and the latch, as well as provide eight more lightbulbs. But you might not be willing to make that investment quite yet.
Of course, I wouldn't even mention these problems unless I knew we were going to solve them eventually. But the problem I want to focus on first is yet another. What if you didn't need to add 100 numbers together in one big sum? What if instead you wanted to use an automated adder to add 50 pairs of numbers to get 50 different sums? Or maybe you'd like a machine versatile enough to add pairs of numbers together, or 10 numbers together, or 100. And you want all the results to be available for your convenient perusal.
The automated adder shown previously displays the running total on a set of lightbulbs attached to the latch. This approach is no good if you want to add 50 pairs of numbers together to get 50 different sums. Instead, you probably want the results to be stored back in the RAM array. That way, you can use the RAM control panel to examine the results at your convenience. That control panel has its own lightbulbs specifically for this purpose.
What this means is that we can get rid of the lightbulbs connected to the latch. But instead, the output from the latch must be connected to the data input of the RAM array so that the sums can be written into the RAM:
I've eliminated some other parts of the automated adder in this diagram as well, specifically the oscillator and the Clear switch. I removed them because it's no longer at all obvious where the Clear and Clock inputs to the counter and the latch will come from. Moreover, now that we've made use of the RAM data inputs, we need a way to control the RAM Write signal.
So let's not worry about the circuit for a moment and instead focus on the problem we're trying to solve. What we're trying to do here is configure an automated adder so that it's not restricted merely to accumulating a running total of a bunch of numbers. We want to have complete freedom in how many numbers we add and how many different sums are saved in RAM for later examination.
For example, suppose we want to add three numbers together and then add two numbers together and then add another three numbers together. We might imagine typing these numbers into the RAM array beginning at address 0000h so that the contents of the memory look like this:
This is how I'll be showing a section of memory in this book. The boxes represent the contents of the memory. Each byte of memory is in a box. The address of that box is at the left. Not every address needs to be indicated because the addresses are sequential and you can always figure out what address applies to a particular box. At the right are some comments about this memory. These particular comments indicate that we want the automated adder to store the three sums in the empty boxes. (Although these boxes are empty, the memory isn't necessarily empty. Memory always contains something, even if it's just random data. But right now it doesn't