(Solved): a) As part of a digital clock, we want to create a sequential clocked circuit to display the curren ...

a) As part of a digital clock, we want to create a sequential clocked circuit to display the current minutes digit. Minutes go from 0 to 9 and back to 0 . The 4-bit signal \( \mathrm{cm}\left(\mathrm{cm}_{3}\right. \) is the MSB of \( \mathrm{cm}, \mathrm{cm}_{0} \) is the LSB of \( \left.\mathrm{cm}\right) \) indicates the current minutes in binary. Minute 0 is indicated by \( \mathrm{cm}= \) " 0000 ", 1 by \( \mathrm{cm}=" 0001^{\prime \prime}, \ldots, 9 \) by \( \mathrm{cm}=" 1001^{\prime \prime} \), etc. Assume the signal \( \mathrm{cm} \) takes the value 0000 on reset (minutes 0 ). Then, the signal \( \mathrm{cm} \) should increment by one at each clock cycle (each clock cycle represents one minute) up to the 9 , and then it should restart at 0 at the next clock cycle. We want to realise this behaviour by controlling the signal sel in the circuit below. Write the truth table for the signal sel in function of \( \mathrm{cm} 3, \mathrm{~cm} 2, \mathrm{~cm} 1 \), \( \mathrm{cm0} \) to realise the desired function, using don't cares wherever possible to help circuit simplification.