Addition

In Addition to That… January 26, 2019 by thepigeonfighter This is where we learn how to do addition in the lowest levels of computer architecture. After completing project one you are left with five, 16-bit chips and no real idea where to go next, or why you made them. Luckily, you don’t have to be as smart as the guys who invented the computer in the first place, and you can always just continue on with the course. In project two you are commissioned to build five more chips. Four of them have to do with addition and the fifth one is the main ALU chip of CPU, which I will talk more about in a later post. One question you might have is what exactly do I mean by 16-bit chips. Well, in previous posts I have talked about the NOT and the MUX chip. Both of those would be considered single-bit chips, because you are feeding them one bit (a zero or one) at a time. So a 16-bit version of those can handle inputs of 16-bits at the same time. Why would you want to do that? Other than the obvious speed benefit when using 16 bits, all of the sudden you have the ability to start representing numbers greater than one. In fact, for an unsigned (only positive) 16-bit number can be as large as 65535, which is awesome because I don’t know about you but I am ready to get back to the real world where 1+1 = 2 despite what Boolean Algebra tries to tell you. But before we ascend to the world of comfort and normalcy that normal arithmetic offers, we must descend back into the weird world of binary. Let me give you a couple examples of how some of these 16-bit chips work. ...

Muxtopia January 26, 2019 by thepigeonfighter My last post introduced the trivial but necessary “Not” chip. Before I move away from the first project I would like to mention one last chip that I found intriguing and especially difficult to solve. That chip is called a “Multiplexer” chip, or a “Mux” chip for short. This chip has a much more complicated specification than the “Not” chip. How it works The mux chip has three inputs which I will refer to as ‘a’, ‘b’, and ‘sel’ short for selector. The mux chip also has just a singular output. The functionality that we want from this chip is when the ‘sel’ input is 0 the out should equal ‘a’. If ‘sel’ is 1 the output should equal ‘b’. Therefore from that information we can derive the following truth table. ...