Draw the equivalent circuit using only NAND gates

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Fatima Hasan
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Homework Statement


For the circuit shown below , draw the equivalent NAND gates .
Logic circuit diagram: inputs A and B feed an XOR gate, whose output and a NOR-type input labelled ~C feed a NOR gate; inputs D and E feed a NAND gate, whose output and ~F feed an XNOR gate; inputs G and H feed an AND gate; three outputs combine in an OR gate producing X.


Homework Equations


-

The Attempt at a Solution


Logic circuit built entirely from NAND gates, with inputs A, ~B, ~A, B, C, D, E, ~F, G and H, and a single output on the right; some connecting wires are drawn in red.

Could someone check my answer please ?
 
Attachments
  • Logic circuit diagram: inputs A and B feed an XOR gate, whose output and a NOR-type input labelled ~C feed a NOR gate; inputs D and E feed a NAND gate, whose output and ~F feed an XNOR gate; inputs G and H feed an AND gate; three outputs combine in an OR gate producing X.
    1.png
    1.5 KB · Views: 1,291
  • Logic circuit built entirely from NAND gates, with inputs A, ~B, ~A, B, C, D, E, ~F, G and H, and a single output on the right; some connecting wires are drawn in red.
    2.png
    2.1 KB · Views: 1,100

Discussion

It is correct.
Are you allowed -A, or -B without using a NAND to invert them?
Are you allowed to use a 3-input NAND?
 
I know one can reproduce any other gate using only NAND gates, but there are some things I don't understand about the above.
  • if ~ means inverted, what is the point in the problem specifying ~C as an input? Why not simply C?
  • does A,B translate into A,~B; ~A,B implicitly, without needing to be shown?
  • is the change from ~C to C just a typo? Or a mis-transcription from the problem? (I guess it has no material effect on the result)
 
Last edited:
Hello @DaveC426913:

The tilda (~) is among the common notations for "not".
Only the author would know why ~C was specified instead of C - but I imagine it was just part of the exercise.
Your second question is basically the same as my 2nd question. You can change A to ~A with a single nand gate. But do the homework instructions require that the gates for generating ~A and ~B be included in the answer?
When @Fatima Hasan specified C instead of ~C in his response, it could not have been "just a typo". Only C would work in his answer. But again, is he allowed to presume that C is available?
 
Last edited:
.Scott said:
It is correct.
Are you allowed -A, or -B without using a NAND to invert them?
Are you allowed to use a 3-input NAND?
Yes to both questions.
 
.Scott said:
But do the homework instructions require that the gates for generating ~A and ~B be included in the answer?
No , only the final answer is required.
 
Here's how I changed from ~C to C :
Four-stage logic circuit diagram of gates on A, B, C, D, E, F, G and H, with output X; the two highlighted sections show an XOR gate with ~C replaced by a single C-input gate.
 
Attachments
  • Four-stage logic circuit diagram of gates on A, B, C, D, E, F, G and H, with output X; the two highlighted sections show an XOR gate with ~C replaced by a single C-input gate.
    Untitled.png
    14.4 KB · Views: 1,028
Fatima Hasan said:
Here's how I changed from ~C to C :
OK but C is not what is provided as input.
The input is ~C. You don't get to change that.

I think this answer is wrong.
 
Fatima Hasan said:
Here's how I changed from ~C to C :
View attachment 235192
I didn't check the rest of your work, but the vertical inverter gate is drawn upside-down...

Logic circuit schematic with a NOR gate fed by input C at the top, an inverter below it, and an XOR gate with input F, whose outputs feed an OR gate at the right.
 
Attachments
  • Logic circuit schematic with a NOR gate fed by input C at the top, an inverter below it, and an XOR gate with input F, whose outputs feed an OR gate at the right.
    upload_2018-12-4_7-1-17.png
    2 KB · Views: 637
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