1,803 views

Design a logic circuit to convert a single digit BCD number to the number modulo six as follows (Do not detect illegal input):

- Write the truth table for all bits. Label the input bits $I_1, I_2, \ldots$ with $I_1$ as the least significant bit. Label the output bits $R_1, R_2\ldots$ with $R_1$ as the least significant bit. Use $1$ to signify truth.
- Draw one circuit for each output bit using,
, two two-input AND gates, one two-input OR gate and two NOT gates.*altogether*

## 3 Answers

Best answer

$${\begin{array}{|cccc|c|ccc|}\hline

\bf{I_4}& \bf{I_3}& \bf{I_2}&\bf{ I_1}& &\bf{R_3}& \bf{R_2} & \bf{R_1}\\\hline

0&0&0&0&\bf{0} &0&0&0\\\hline 0&0&0&1&\bf{1}& 0&0&1 \\ \hline 0&0&1&0&\bf{2}& 0&1&0 \\ \hline 0&0&1&1&\bf{3}& 0&1&1 \\ \hline 0&1&0&0&\bf{4}& 1&0&0 \\ \hline 0&1&0&1&\bf{5} &1&0&1 \\ \hline 0&1&1&0&\bf{6}& 0&0&0 \\ \hline0&1&1&1&\bf{7}& 0&0&1\\ \hline 1&0&0&0&\bf{8}& 0&1&0 \\ \hline 1&0&0&1&\bf{9}& 0&1&1 \\ \hline

\end{array}}$$

- $R_1 = I_1$
- $R_2 = I_2\overline{ I_3} + I_4$
- $R_3 = I_3\overline{I_2}$

This requires $2$ NOT gates, $2$ two-input AND gates and $1$ two-input OR gate.