It's probably worth at least mentioning that the applications discussed here only scratch the surface of what transistors can do. In switching application transistors are always either "totally off" or "totally on." But they have an "active region" in between, and in that region they can function as amplifiers, components of filters, and so on. That was really the "earliest" applications of transistors, e.g. in transistor radios and so on. The computing applications became prominent later.
11:30 - Deciding which is "primary" is much like choosing a coordinate system in a physics problem; you can make any choice you want. One common point of view is to use the NAND gate (AND with a NOT tacked on) - you can make ANY FUNCTION YOU WANT using only NANDs.
Thank you for the really inspiring series! Nevertheless, as far as I know, the current state of the art is NAND gates, and the theory is built around Sheffer stroke so any logic table can be implemented using just one building block. And it takes just two transistors (of any technology, perhaps TTL requires something special if I remember well) to make the NAND gate. A minimal number of transistors and a minimal number of building blocks are mandatory for the scalable and efficient manufacturing process. So, XOR and AND introduction should offer something really exciting to be attractive. Looking forward to the next episodes to learn what exactly! Thanks again!
Hi Vlad: I'd like to emphasize that I am not really advocating using certain types of gates over others when it comes to building circuits. I am advocating a mathematical foundation of the subject which is based on the AND and XOR gates, or mathematically the mod 2 arithmetic encoded in the bifield B_2. No matter what gates are technically convenient for us, depending perhaps on how easy they are to build, what materials are used etc. I want the mathematics to be the most natural. Unfortunately that is not the Boolean algebra that the current framework uses. Even on some distant planet, with completely different semiconductor materials etc, I reckon the Algebra of Boole would provide the best mathematical framework.
Sure, I understand your point. I just want to say that this particular subject is very close to the manufacturing, and, maybe, won't be convenient even if its framework is better. I really admire your works about the real numbers, which are really blur everything, including computer operation. I myself spent a lot of time explaining to people why we need algorithms and not abstract ideas.
Although the Sheffer stroke (NAND, or alternatively its dual) can be used as the sole element to combine to mimic all other operators of propositional calculus, the combinations aren't necessarily optimum. If your technology naturally creates cheap NAND gates then it makes sense to use those gates. USB "flash drives" and RAM disks are usually based on NANDs, not because of mathematical aesthetics but because of economy.
It's probably worth at least mentioning that the applications discussed here only scratch the surface of what transistors can do. In switching application transistors are always either "totally off" or "totally on." But they have an "active region" in between, and in that region they can function as amplifiers, components of filters, and so on. That was really the "earliest" applications of transistors, e.g. in transistor radios and so on. The computing applications became prominent later.
11:30 - Deciding which is "primary" is much like choosing a coordinate system in a physics problem; you can make any choice you want. One common point of view is to use the NAND gate (AND with a NOT tacked on) - you can make ANY FUNCTION YOU WANT using only NANDs.
Thank you for the really inspiring series! Nevertheless, as far as I know, the current state of the art is NAND gates, and the theory is built around Sheffer stroke so any logic table can be implemented using just one building block. And it takes just two transistors (of any technology, perhaps TTL requires something special if I remember well) to make the NAND gate. A minimal number of transistors and a minimal number of building blocks are mandatory for the scalable and efficient manufacturing process. So, XOR and AND introduction should offer something really exciting to be attractive. Looking forward to the next episodes to learn what exactly! Thanks again!
Hi Vlad: I'd like to emphasize that I am not really advocating using certain types of gates over others when it comes to building circuits. I am advocating a mathematical foundation of the subject which is based on the AND and XOR gates, or mathematically the mod 2 arithmetic encoded in the bifield B_2. No matter what gates are technically convenient for us, depending perhaps on how easy they are to build, what materials are used etc. I want the mathematics to be the most natural. Unfortunately that is not the Boolean algebra that the current framework uses. Even on some distant planet, with completely different semiconductor materials etc, I reckon the Algebra of Boole would provide the best mathematical framework.
Sure, I understand your point. I just want to say that this particular subject is very close to the manufacturing, and, maybe, won't be convenient even if its framework is better.
I really admire your works about the real numbers, which are really blur everything, including computer operation. I myself spent a lot of time explaining to people why we need algorithms and not abstract ideas.
Although the Sheffer stroke (NAND, or alternatively its dual) can be used as the sole element to combine to mimic all other operators of propositional calculus, the combinations aren't necessarily optimum. If your technology naturally creates cheap NAND gates then it makes sense to use those gates. USB "flash drives" and RAM disks are usually based on NANDs, not because of mathematical aesthetics but because of economy.