A divide by 78 counter can be realized using? a) 6 number of mod 13 counters b) 13 number of mod 6 counters c) one mod-13 counter followed by one mod 6 counter d) 13 number of mod-13 counters The right answer is C. 78=13*6. The mod-13 counter will be incremented with each pulse of the incoming signal, and will overflow every 13 counts of such pulses. The mod-6 counter will be incremented each time that the mod-13 counter overflows. The mod-6 counter will overflow every 6 of its counts. Therefore, the mod-6 counter will overflow every 6*13=78 pulses of the incoming signal. In other words, for each state of the mod-6 counter, the mod-13 counter counts 13 states. So, in total, you will have 6*13=78 different "global" states. That's why, if you have them one after the other (so that counter k increments one unit when counter k-1 overflows), you have to multiply the numbers of states, not add them. These will be the count values for each of the two counters, before each pulse at the input. Code: {(mod-13 counter value) (mod-6 counter value)} {0 0} {1 0} ... {12 0} {0 1} {1 1} ... {12 1} {0 2} {1 2} ... ... {12 5} <-- Here is the overflow for the global counter formed. Above this line, there are 78 different states. {0 0} ...