Converting logic diagram to only NAND gates

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Homework Help Overview

The discussion revolves around the conversion of logic diagrams specifically focusing on the use of NAND gates as inverters. Participants are exploring the properties of NAND gates and their functionality in digital logic design.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning how a NAND gate can function as an inverter, particularly regarding the requirement of two inputs. There is an exploration of tying inputs together and the implications for the output. Some participants are revisiting previous discussions on this topic and clarifying the conditions under which a NAND gate can act as a NOT gate.

Discussion Status

The discussion is active with participants providing insights into the behavior of NAND gates when inputs are tied together. There is an exchange of ideas regarding the truth table of NAND gates and alternative methods to achieve inversion using NAND gates. No consensus has been reached, but several productive lines of reasoning are being explored.

Contextual Notes

Participants are reflecting on previous threads and discussions, indicating a continuity in the learning process. There may be assumptions about prior knowledge that are influencing the current conversation.

LongApple
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Homework Statement



How is he able to just swap the inverter for a NAND gate? Doesn't a NAND gate require two things?

See the text on the right for his explanation
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Homework Equations

The Attempt at a Solution

 
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LongApple said:
How is he able to just swap the inverter for a NAND gate? Doesn't a NAND gate require two things?
What sort of "things" did you have in mind? If the inputs are tied together then the only inputs available to the NAND are both inputs "1" or both inputs "0". What does a NAND gate output for each case?
 
LongApple said:
How is he able to just swap the inverter for a NAND gate?
So, we are revisiting this topic! :) We thought you would learn about the NAND inverter from your previous thread, but I think you dropped out and didn't see it through to its conclusion.

You can join the two inputs together, which gives both inputs either 1 or both inputs 0, and the output becomes the NOT of this. So, yes, a NAND gate with a signal applied to both its inputs acts as a NOT gate.
 
Or look at it this way.. The NAND truth table is

00=1
01=1
10=1
11=0

if both inputs are wired together they are always the same, so the only combinations that can occur are..

00=1
11=0

There is another way to turn a NAND gate into an inverter - You could just connect one input to a logic 1 permanently...

10=1
11=0
 

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