# Making 2-input AND gate, 2-input OR gate and NOT gate using only the “SAND” gate

Suppose there is a special gate called a SAND gate (Single-inversion AND) that looks like this:

How can I make 2-input AND gate, 2-input OR gate and NOT gate using only the SAND gate?

The truth table for this gate is:

$$\begin{array}{|c|c|c|} \hline A & B & \overline{A}\ {B} \\ \hline 0 & 0 & 0\\ \hline 0 & 1 & 1\\ \hline 1 & 0 & 0\\ \hline 1 & 1 & 0\\ \hline \end{array}$$

To make a 2-input AND gate using only SAND gates, I would have to put 2 SAND gates in a row. Is this correct?

I don't know how to make 2-input OR gate and NOT gate using SAND gates. Can you give me a hint please?

Edit: I am only allowed to use SAND gates.

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Is there any limitation in the number of gate you can use? –  Amit Hasan Aug 16 '14 at 8:46

Let $\text{SAND}(A,B) = \overline{A}B$

NOT gate
$\overline{A} = \overline{A}.1 = \text{SAND}(A,1)$
Connect B to '1' and feed input to A.

AND gate
$AB = \overline{(\overline{A})}B= \overline{(\text{SAND}(A,1))}B = \text{SAND}(\text{SAND}(A,1),B)$
Invert the 1st input (using NOT gate implemented above) before feeding to SAND.

OR gate
\begin{align}A+B & = \overline{(\overline{A}\ \overline{B})}\\ & = \text{SAND}(\overline{A}\ \overline{B},1)\\ & = \text{SAND}(\overline{A}. \text{SAND}(B,1),1)\\ & = \text{SAND}(\text{SAND}(A,\text{SAND}(B,1)),1)\end{align}
Invert the 2nd input before feeding to SAND and feed its output to another inverter.

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Thank you for the answer nidhin. Unfortunately, I cannot use NOT gates, I need to use only SAND gates. So my answer should have only the following gates: i.imgur.com/wutc3kR.png –  user51414 Aug 16 '14 at 8:30
The top one is the one that gets inverted, so the link I provided should look like this i.imgur.com/6JQAw4B.png –  user51414 Aug 16 '14 at 8:43
I want to upvote your answer but I cannot because I don't have 15 points :( –  user51414 Aug 16 '14 at 8:46
nidhin didn't use a NOT gate, he implemented a NOT gate using the SAND. –  Mike Aug 16 '14 at 8:46
@user2357111317192329 please see the edited answer. –  nidhin Aug 16 '14 at 8:47