lecture 13

8.1 Introduction:
A counter is an electronic device which is able to generate an orderly
sequence of binary numbers. The addresses which command digital circuits as
decoder, multiplexer, demultiplexer etc. are most of the time generated by counters.
There two main basic types of counters: asynchronous counter and synchronous
counter. Counters are designed using flip-flops, usually J-K flip-flops.
Asynchronous counters functions in such a way that the clock signal does not
affect all the flip-flops at the same instant; in fact, the clock signal triggers the first flipflop which in his turn trigger the second flip-flop using its output signal. The second
flip-flop in his turn will trigger the third one, and so on, till the last flip-flop. It is just like
the triggering signal was being propagated from the first flip-flop to the last. For this
reason, asynchronous counters are also called propagation counters.
The flip-flops of a synchronous counter are all triggered by the same clock
signal at the same instant. In fact, all the flip-flops function in synchronism with the
clock signal. The outputs of all the flip-flops change their status at the same instant.
8.2 Asynchronous counters:
Let us consider the following binary count sequence. The numbers are coded
in four bits. Q0 is the LSB and Q3 is the MSB. It can be noticed that each bit in this
four-bit sequence toggles when the bit before it (the bit having a lesser significance or
place weight), toggles from 1 to 0. Small arrows are used to indicate those places in
the above count sequence. So, to design an asynchronous counter which is able to
generate the above sequence of numbers, we need to determine how to connect the
clock inputs of each of the four J-K flip-flops (each flip-flop generating one bit) in such
a way that each bit will toggle only when the bit just before it is transitioning from 1 to
0. The easier way of doing that is to use flip-flops with negative edge triggering. The
clock input of each flip-flop will simply be connected to the non-complemented output
Q of the flip-flop situated just before it (Flip-flop having one lesser place weight). In
this condition, each flip-flop will toggle any time the output of the flip-flop one place
lesser weighted than it is transitioning from 1 to 0 (negative edge).