## 5 Answers

There are two conditions for a function being self dual.

- it should be a neutral function. (no. of minterms = no. of max terms)
- no two mutually exclusive terms should be there like $($$0-7$ are mutually exclusive $1-6, 2-5, 3-4$$)$ from these pairs only one should be there.

Clearly, there are $4$ minterms, so number of minterms = no. of maxterms.

And second condition is also satisfied. So, it is a self dual function .

**(b) Excess-3 to BCD**

$$\overset{\textbf{Truth Table}}{\begin{array}{|cccc|cccc|} \hline \rlap{\textbf{Inputs}}&&&&\rlap{\textbf{Outputs}}\\ \hline \textbf{W} & \textbf {X} &\textbf {Y} & \textbf {Z} & \textbf{A}&\textbf {B} & \textbf {C} & \textbf{D} \\\hline0&0&1&1&0&0&0&0\\\hline0&1&0&0&0&0&0&1\\\hline0&1&0&1&0&0&1&0 \\\hline 0&1&1&0&0&0&1&1 \\\hline0&1&1&1&0&1&0&0 \\\hline 1&0&0&0&0&1&0&1\\\hline1&0&0&1&0&1&1&0\\\hline1&0&1&0&0&1&1&1 \\\hline 1&0&1&1&1&0&0&0 \\\hline1&1&0&0&1&0&0&1 \\\hline \end{array}}$$

**MAPS:**

### 3 Comments

@Gate Fever No you are wrong. Xs-3 code is for BCD. So we need to just add 3 to 0 - 9 digits i.e. 0+3 to 9+3 = 3 to 12.

a) It is a self dual function, because it satisfies both conditions of self dual fuction

->It should be neutral (i.e no. of minterms is equal to the no. of maxterms)

->The function does not contain two mutually exclusive term ( eg ABC mutually exclusive to A'B'C' , AB'C' mutually excluseive to A'BC)

b) Excess-3 to BCD converter

Ref http://www.sukanta.info/wp-content/uploads/2012/05/Excess-3-code-to-bcd-converter3.pdf