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Counters

Counter circuits based on flip-flops are widely used in Digital Systems. Besides counting, these counters are used as frequency dividers and with minor changes in the circuit they are used as shift registers. Counters are classified as Asynchronous and Synchronous counters. Asynchronous counters as the name indicates are not triggered simultaneously. The multiple flip-flops that are connected together to form a counter circuit do not receive the triggering clock signal simultaneously. The flip-flop that represents the least significant count bit of the n-bit counter is connected to the clock signal, the remaining flip-flops receive their clock signals form the outputs of the preceding flip-flops connected in the counter circuit. The clock signal thus ripples through successive flip-flops. Synchronous counters on the other hand have all the clock inputs of the multiple flip-flops connected to a common clock signal. All the flip-flops in a Synchronous counter receive clock signals simultaneously.

Asynchronous and Synchronous are further classified as up counters or down counters depending upon the sequence in which they count. They are further classified in terms of the number of states or the range of numbers to which the counters can count.

Asynchronous Counters (Ripple Counters)

Asynchronous counters are implemented by connecting together multiple flip-flops together. The triggering clock signal is connected to the clock input of the first flip-flop. The

clock inputs of the remaining flip-flops are connected to the Q or Q output of the previous flip-flop. On a clock transition at the clock input of the first flip-flop the output state of the flip-flop changes. With the transition in the output state of the first flip-flop, there is also a transition at the clock input to the second flip-flop as the output of the first flip-flop is connected to the clock input of the second flip-flop. Due to the clock transition the second flip-flop changes its output state. The change in the output state of the second flip-flop occurs after the first flip-flop changes its state. Similarly, the last flip-flop connected in the counter circuit changes its output state after the output of the flip-flop connected to its clock input has changed it state. The outputs of the flip-flops change in a sequence as the clock signal propagates through the flip-flops as they change their output states one after the other. The Asynchronous counters are also known as Ripple Counters due to the rippling effect of the clock signal.

A three-bit Asynchronous counter circuit is shown in Figure 26.4. In the circuit diagram

shown the Q output of each is connected to the clock input of the next flip-flop. The J-K inputs of each of the three flip-flop are connected to logic high allowing the flip-flop to toggle their output state on a high to low transition at their clock input.

The output state of the first flip-flop toggles at every positive to negative clock transition in intervals t1 to t8. The output F1 of the second flip-flop toggles at intervals t2, t4, t6 and t8 on every high to low transition of the output F0. The output F2 toggles its output state at intervals t4 and t8 on a high to low transition of the flip-flop output F1.

Figure 26.4a 3-bit Asynchronous Up-Counter

CLOCK Input

F0 Output

F1 Output

F2 Output

Figure 26.4b Timing Diagram of a 3-bit Asynchronous Up-Counter

Table 26.1 Output State of a 3-bit Asynchronous Up-Counter

Propagation Delay

The timing diagram shown in figure 26.4b doesn’t take into account the propagation delay that occurs between each clock input and the corresponding toggling output. The timing diagram which takes into account the propagation delay is shown in figure 26.5. At time interval t4 on a clock transition the output F0 toggles to a new state after a delay determined by tPHL propagation delay of the first flip-flop. At interval t5 on the high to low transition of the F0 output, the output F1 toggles to a new state after a propagation delay tPHL of the second flip-flop. Finally, at interval t6 the transition in F1 output toggles the output F2 of the third flip-flop. The output F2 becomes stable after a propagation delay tPLH of the third flip-flop. The propagation delay of each of the three flip-flop adds up to delay the output F2 by three propagation delays with respect to the clock transition at interval t4. If the counter circuit is extended by adding more flip-flops, then the output of the last flip-flop might exceed the clock period of the clock which causes timing problems. The Asynchronous counters can not work at high clock frequencies and cause problems with decoding circuits.

CLOCK Input

F0 Output

F1 Output

F2 Output

Figure 26.5 Timing Diagram of a 3-bit Asynchronous with propagation delay

The timing diagram of the 3-bit counter circuit using a clock of a higher frequency is shown in Figure 26.6a. At interval t4, the negative clock transition toggles the F0 output to logic low at interval tA after a propagation delay of tPHL. The negative transition of F0 at tA toggles the F1 output to logic low at interval t5 after a propagation delay of tPHL. Finally, the F2 output is toggled to logic high at interval tB after a delay of tPLH after the clock (F1) transition at interval t5. The output states of the counter at intervals t1 to t7 are shown in table 26.2. The output at interval t5 should be 100 instead of 010.

Figure 26.6a Timing Diagram of a 3-bit Asynchronous with high frequency clock

Table 26.2 Output of a 3-bit Asynchronous Up-Counter with high frequency clock

Mod-n Counters

The term Mod represents the Modulus of the counter which is the total number of unique states through which the counter will sequence through. A 3-bit Asynchronous counter can count up from 0 to 7 or count down from 7 to 0. The 3-bit counter has 8 different states represented by the 8 outputs 0 to 7. The counter states or the range of numbers of a counter is determined by the formula 2^m. where m represents the number of flip-flops. Therefore, a Mod8 counter implemented using three flip-flops 2³ has 8 output states.

Counter can also be designed to have less number of states than 2^m. The resulting sequence is called a truncated sequence. The counter therefore counts up to the truncated sequence. Designing a truncated sequence counter is very simple. When the counter counts up to the intended sequence it is reset to the initial count value 0. The counter is reset to the initial count value by activating the Clear asynchronous inputs. The clears input is activated by the counter through a combinational circuit that activates its output when the appropriate count sequence is reached. The Mod-6 counter is shown in figure 26.7.

Figure 26.7a Mod-6 Counter

Figure 26.7b Timing diagram of a Mod-6 Counter

The counter counts from state 000 to 101. At interval t6 the counter counts to 110. The outputs F1 and F2 of the counter are connected to the inputs of a 2-input NAND gate, which sets its output to logic zero when both its inputs become logic 1 at interval t6. The output of the NAND gate is connected to the three active-low asynchronous Clear input of the three flip-flops which are set to low by the NAND gate. Therefore the counter is immediately reset to state 000 from where it proceeds to sequence through the count values. The Mod number of the counter also determines the frequency at the output of the counter. The output at F2 has a frequency which is 1/6^th of the input clock frequency. Thus Mod-n counters can be design to generate 1/n^th frequency signal with respect to the input clock signal.

Mod-10 Counter (Decade Counter)

A decade counter uses four-flip-flops to implement the circuit which counts up to 10 unique states (0000 to 1001). The counter is reset when it counts to the next state 1010. The frequency of the output signal is 1/10^th the input clock frequency. Figure 26.8.

Figure 26.8a Asynchronous Decade Counter

Figure 26.8b Timing diagram of a Decode Counter

The output F1 and F3 are connected through a NAND gate to the active-low clear inputs of all the four flip-flops. The counter counts from 0000 to 1001 (ten output states), when it counts to 1010, the output of the NAND gate is set to logic low which resets all the four flip-flops to state 0000.

Integrated Circuit Asynchronous Counters

Asynchronous Counters are available in Integrated Circuit form. The 74LS93A is a 4-bit Asynchronous Counter. The counter has two separate clock inputs CLK A and CLK B connected to the clock input of the first and second flip-flop respectively. The second, third and fourth flip-flops are internally connected as a ripple 3-bit counter. The counter also has two inputs pins connected to the inputs of a 2-input NAND (internal) gate, the output off which is connected to the clear inputs of all the four flip-flops. The counter provides four outputs, one form each flip-flop. Figure 26.9

The 74LS93A can be configured as MOD-16 counter by connecting CLK B input pin to the Q0 output pin of the IC. RO 1 and RO 2 are connected to logic low. A Decade counter can be implemented by connecting CLK B input to the Q0 and Q1 and Q3 outputs to RO 1 and RO 2 respectively. Figure 26.10 Two 74LS 93As ca be cascaded together to form a larger counter. A MOD-50 counter is implemented using two 74LS93A ICs. Figure 26.11

CLKA CLKB

^Q₀

^Q₁

^Q₂

^Q₃

Figure 26.10b 74LS93A connected as Decade Counter

In the circuit diagram two 74LS93As are connected together to form a frequency divider which divides the input frequency by 50. The first 74LS93A is connected to divide the input frequency by 10. The Q3 output of the first 74LS93A is connected to the CLKB input of the second 74LS93A. The second 74LS93A is connected to divide the input frequency at CLKB by 5. The Q3 output of the second 74LS93A therefore provides an output which is 1/50^th of the clock applied at the CLKA input of the first 74LS93A. The second 74LS93A requires the use of only three flip-flops, therefore the first flip-flop with clock input CLKA is left unconnected.