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I was asked to implement a logic expression (F = A'B' + C'D' + AC') with AND-OR-INVERT(AOI) gates. I made the circuit (Figure 1) below, but I looked it up on Wikipedia and found that AOI gates are made out of two AND gates and a single NOR gate. I made the second circuit (Figure 2,) but their outputs were different even though their inputs were the same. I would really appreciate it if someone could explain this to me.

Figure 1

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Figure 2

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  • \$\begingroup\$ Are you only allowed to use and-or-invert gates? Or are other gates permitted? \$\endgroup\$
    – jonk
    Commented Nov 15, 2020 at 6:55
  • \$\begingroup\$ Yes, but im not sure if and-or-inverter means and, or, not gates or and, nor gates. \$\endgroup\$
    – Kalamakra
    Commented Nov 15, 2020 at 9:07
  • \$\begingroup\$ Well, if you put the same input value into all four inputs then the output will be the inverted input value. I'm curious what you are allowed. That's not clear to me, yet. \$\endgroup\$
    – jonk
    Commented Nov 15, 2020 at 9:10
  • \$\begingroup\$ We are only allowed to use AND-OR-INVERT gates. \$\endgroup\$
    – Kalamakra
    Commented Nov 15, 2020 at 10:51

1 Answer 1

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Your first gate realization does indeed implement \$F =A'B' +C'D' + AC' \$.

As far as I can see, your second circuit implements $$F =(AB +CD)' + AC' =(AB)'(CD)'+AC'$$

Those two expressions are not equivalent, so identical inputs yield different outputs.

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  • \$\begingroup\$ Yes thats why I'm getting different outputs, but is my first circuit a and-or-invert circuit? \$\endgroup\$
    – Kalamakra
    Commented Nov 15, 2020 at 9:08
  • \$\begingroup\$ Yes, your first circuit only utilizes AND-gates, OR-gates and inverters. A so-called AND-OR-Invert realization. \$\endgroup\$
    – Carl
    Commented Nov 15, 2020 at 9:11

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