making a circuit using a given formula

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bttshrbs

Joined Oct 30, 2017
1
I'm sorry in advance if some of this doesn't make sense I've never written about this kind of topic in english.
So for homework I had to minimize a formula which I did, but now I have to make that new formula into a circuit using only NAND and then using only NOR. I've been stuck at this for 2 hours I just can't figure it out so please help. The minimized formula is Y=A+B(inverted)+C.
Also the attached photo is what I've done so far if that helps.15094084443192135573266.jpg
 

WBahn

Joined Mar 31, 2012
26,398
One brute force way to do it is to just figure out how to implement the basic gates (NOT, OR, AND) using nothing but NANDs and then nothing but NORs. Then you can just go through gate by gate and replace each basic gate with its NAND-only or NOR-only equivalent. Keep in mind that this will seldom produce an efficient implementation, merely one that works.

The far better (and simpler) way is to see what DeMorgan's says about ANDs followed by ORs.
 

RBR1317

Joined Nov 13, 2010
690
Here is an explanation that focuses more on visual manipulation rather than Boolean algebra. I get good results by first minimizing the logic expression, then adding/removing/sliding inversion circles in the minimized logic diagram to get the all-NAND or all-NOR implementation.
DeMorgan-Theorem_2.png
 
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