Optimal Solution ?

[b1tbull]

Greetings,

I just finished chapter one and this is the most fun I had in Computer Science since learning Z80 assembler on a trs-80 in the 80's ( pun intended ).
Being rather visual in solving the chip designs http://www.cburch.com/logisim/index.html
is an invaluable tool for building the circuit, testing the logic and easily translate it into HDL code.
This was referred to in other posts already , but this is the most actual link.
There is not a single solution for each chip, but some require less parts depending on the usage of high or low level building blocks.
May I suggest as an additional challenge to add the optimal (minimal) number of  parts for each chip to the Project 1 Chips table so one can verify if the found solution is optimal.

Thanks to all involved for this excellent course site.
 

[cadet1620]

Optimization is a multidimensional problem, so there is no single "optimal" solution for most of the parts.

For example, typical Mux solutions use 4 parts; a mix of And, Or and Not. It's also possible to build the Mux from 4 Nands.

Which of those solutions is better? The And/Or/Not solution is much easier to understand, so I would consider it better that the more obscure Nand solution.

In the actual physical implementation, neither of these solutions is used. Modern ICs implement multiplexors using transmission gates.
    
The Not and the transmission gates are 2 transistors each for a total of 6 transistors. A CMOS Nand gate requires 4 transistors.

In most physical implmentations, circuit speed, size, and power are a 3-way tradeoff.


If you mail me your solutions, I will be happy to comment on them.

--Mark

[b1tbull]

Hi Mark,

Thanks for your your feedback. As retired IT professional I am quite new to this exciting low level computer building. I probably misused optimal for smallest sub-components solutions.
It is clear that using complex components will result in less parts than building with simple nand, and, or and not gates.
While solutions are ( and should not be ) published too widely I could not resist to peek at what others came up for each exercise ( thanks to Mr. Google ). For example the DMux8way chip can be build using
either 3 , 5 or 7 "mux" gates according to some solutions I found from other students.
My design resulted in a 3 part chip - beginners luck I guess..
So I wonder if my other designs are as effective ( this is with the lowest number of parts ).

Francis