Flip-Flops and Related Devices
391
Figures 10.34(a) and (b) respectively show the circuit symbols of positive edge-triggered and negative
edge-triggered T flip-flops, along with their function tables.
If we consider the T input as active when HIGH, the characteristic table of such a flip-flop is shown
in Fig. 10.34(c). If the T input were active when LOW, then the characteristic table would be as shown
in Fig. 10.34(d). The Karnaugh maps for the characteristic tables of Figs 10.34(c) and (d) are shown
in Figs 10.34(e) and (f) respectively. The characteristic equations as written from the Karnaugh maps
are as follows:
Q n+1 = TTQ n + T TQ n
(10.19)
Q n+1 = T TQ n + TTQ n
(10.20)
It is obvious from the operational principle of the T flip-flop that the frequency of the signal at the
Q output is half the frequency of the signal applied at the T input. A cascaded arrangement of nT
flip-flops, where the output of one flip-flop is connected to the T input of the following flip-flop, can
be used to divide the input signal frequency by a factor of 2
n . Figure 10.35 shows a divide-by-16
circuit built around a cascaded arrangement of four T flip-flops.
10.6.1 J-K Flip-Flop as a Toggle Flip-Flop
If we recall the function table of a J -K flip-flop, we will see that, when both J and K inputs of the
flip-flop are tied to their active level (‘1’ level if J and K are active when HIGH, and ‘0’ level when J
and K are active when LOW), the flip-flop behaves like a toggle flip-flop, with its clock input serving
as the T input. In fact, the J -K flip-flop can be used to construct any other flip-flop. That is why it is
also sometimes referred to as a universal flip-flop. Figure 10.36 shows the use of a J -K flip-flop as a
T flip-flop.
Example 10.5
Refer to the cascaded arrangement of two T flip-flops in Fig. 10.37(a). Draw the Q output waveform
for the given input signal. If the time period of the input signal is 10 ms, find the frequency of the
output signal? If, in the flip-flop arrangement of Fig. 10.37(a), FF-2 were positive edge triggered,
draw the Q output waveform.
Solution
The Q output waveform is shown in Fig. 10.37(b) along with the Q output of FF-1. The output of the
first T flip-flop changes state for every negative-going edge of the input clock waveform. Its frequency
is therefore half the input signal frequency. The output of the first flip-flop acts as the clock input
for the second T flip-flop in the cascade arrangement. The second flip-flop, too, toggles for every
negative-going edge of the waveform appearing at its input. The final output thus has a frequency that
is one-fourth of the input signal frequency:
• Now the time period of the input signal = 10 ms.
• Therefore, the frequency = 100 kHz.
• The frequency of the output signal = 25 kHz.
391
Figures 10.34(a) and (b) respectively show the circuit symbols of positive edge-triggered and negative
edge-triggered T flip-flops, along with their function tables.
If we consider the T input as active when HIGH, the characteristic table of such a flip-flop is shown
in Fig. 10.34(c). If the T input were active when LOW, then the characteristic table would be as shown
in Fig. 10.34(d). The Karnaugh maps for the characteristic tables of Figs 10.34(c) and (d) are shown
in Figs 10.34(e) and (f) respectively. The characteristic equations as written from the Karnaugh maps
are as follows:
Q n+1 = TTQ n + T TQ n
(10.19)
Q n+1 = T TQ n + TTQ n
(10.20)
It is obvious from the operational principle of the T flip-flop that the frequency of the signal at the
Q output is half the frequency of the signal applied at the T input. A cascaded arrangement of nT
flip-flops, where the output of one flip-flop is connected to the T input of the following flip-flop, can
be used to divide the input signal frequency by a factor of 2
n . Figure 10.35 shows a divide-by-16
circuit built around a cascaded arrangement of four T flip-flops.
10.6.1 J-K Flip-Flop as a Toggle Flip-Flop
If we recall the function table of a J -K flip-flop, we will see that, when both J and K inputs of the
flip-flop are tied to their active level (‘1’ level if J and K are active when HIGH, and ‘0’ level when J
and K are active when LOW), the flip-flop behaves like a toggle flip-flop, with its clock input serving
as the T input. In fact, the J -K flip-flop can be used to construct any other flip-flop. That is why it is
also sometimes referred to as a universal flip-flop. Figure 10.36 shows the use of a J -K flip-flop as a
T flip-flop.
Example 10.5
Refer to the cascaded arrangement of two T flip-flops in Fig. 10.37(a). Draw the Q output waveform
for the given input signal. If the time period of the input signal is 10 ms, find the frequency of the
output signal? If, in the flip-flop arrangement of Fig. 10.37(a), FF-2 were positive edge triggered,
draw the Q output waveform.
Solution
The Q output waveform is shown in Fig. 10.37(b) along with the Q output of FF-1. The output of the
first T flip-flop changes state for every negative-going edge of the input clock waveform. Its frequency
is therefore half the input signal frequency. The output of the first flip-flop acts as the clock input
for the second T flip-flop in the cascade arrangement. The second flip-flop, too, toggles for every
negative-going edge of the waveform appearing at its input. The final output thus has a frequency that
is one-fourth of the input signal frequency:
• Now the time period of the input signal = 10 ms.
• Therefore, the frequency = 100 kHz.
• The frequency of the output signal = 25 kHz.