Counter dan Register

Transcription

1 Counter dan Register

2 Introduction Circuits for counting events are frequently used in computers and other digital systems. Since a counter circuit must remember its past states, it has to possess memory. The chapter about flip-flops introduced how flipflops are connected to make a counter. The number of flip-flops used and how they are connected determine the number of states and the sequence of the states that the counter goes through in each complete cycle.

3 Counters Classification Counters can be classified into two broad categories according to the way they are clocked: Asynchronous (Ripple) Counters; the first flip-flop is clocked by the external clock pulse, and then each successive flip-flop is clocked by the Q or Q' output of the previous flip-flop Synchronous Counters; all memory elements are simultaneously triggered by the same clock

4 Asynchronous (Ripple) Counters (twobits) A two-bit asynchronous counter is shown on the right. The external clock is connected to the clock input of the first flip-flop (FF0) only.

5 Asynchronous (Ripple) Counters (two-bits) FF0 changes state at the falling edge of each clock pulse, but FF1 changes only when triggered by the falling edge of the Q output of FF0. Because of the inherent propagation delay through a flipflop, the transition of the input clock pulse and a transition of the Q output of FF0 can never occur at exactly the same time. Therefore, the flip-flops cannot be triggered simultaneously, producing an asynchronous operation. Note that for simplicity, the transitions of Q0, Q1 and CLK in the timing diagram above are shown as simultaneous even though this is an asynchronous counter. Actually, there is some small delay between the CLK, Q0 and Q1 transitions.

6 Asynchronous (Ripple) Counters (two-bits) The 2-bit ripple counter circuit above has four different states, each one corresponding to a count value. Similarly, a counter with n flip-flops can have 2 to the power n (2 n ) states. The number of states in a counter is known as its mod (modulo) number. Thus a 2-bit counter is a mod-4 counter.

7 Asynchronous (Ripple) Counters (threebits) It works exactly the same way as a two-bit asynchronous binary counter mentioned above, except it has eight states due to the third flip-flop.

8 Asynchronous Decade Counters The binary counters previously introduced have two to the power n (2 n ) states. But counters with states less than this number are also possible. They are designed to have the number of states in their sequences, which are called truncated sequences. A common modulus for counters with truncated sequences is ten. A counter with ten states in its sequence is called a decade counter.

9 Asynchronous Decade Counters Once the counter counts to ten (1010), all the flip-flops are being cleared. Notice that only Q1 and Q3 are used to decode the count of ten. This is called partial decoding, as none of the other states (zero to nine) have both Q1 and Q3 HIGH at the same time.

10 Asynchronous Decade Counters The sequence of the decade counter is shown in the table below:

11 Asynchronous Up-Down Counters In certain applications a counter must be able to count both up and down. The circuit below is a 3-bit up-down counter. It counts up or down depending on the status of the control signals UP and DOWN.

12 Synchronous Counters In synchronous counters, the clock inputs of all the flip-flops are connected together and are triggered by the input pulses. Thus, all the flip-flops change state simultaneously (in parallel).

13 Synchronous Counters

14 Synchronous Counters The most important advantage of synchronous counters is that there is no cumulative time delay because all flip-flops are triggered in parallel. Thus, the maximum operating frequency for this counter will be significantly higher than for the corresponding ripple counter.

15 Synchronous Decade Counters Similar to an asynchronous decade counter, a synchronous decade counter counts from 0 to 9 and then recycles to 0 again. This is done by forcing the 1010 state back to the 0000 state.

16 Synchronous Decade Counters From the sequence on the left, we notice that: Q0 toggles on each clock pulse. Q1 changes on the next clock pulse each time Q0=1 and Q3=0. Q2 changes on the next clock pulse each time Q0=Q1=1. Q3 changes on the next clock pulse each time Q0=1, Q1=1 and Q2=1 (count 7), or when Q0=1 and Q3=1 (count 9).

17 Synchronous Up-Down Counters A circuit of a 3-bit synchronous up-down counter and a table of its sequence are shown below.

18 Applications Digital counters are very useful in many applications. They can be easily found in digital clocks and parallel-to-serial data conversion (multiplexing). A group of bits appearing simultaneously on parallel lines is called parallel data. A group of bits appearing on a single line in a time sequence is called serial data. Parallel-to-serial conversion is normally accomplished by the use of a counter to provide a binary sequence for the data-select inputs of a multiplexer.

19 Parallel-to-serial conversion

20 Register Types The basic types of shift registers Serial In - Serial Out Serial In - Parallel Out Parallel In - Serial Out Parallel In - Parallel Out bidirectional shift registers A special form of counter - the shift register counter

21 Serial In - Serial Out Shift Registers (1) A basic four-bit shift register can be constructed using four D flip-flops

22 Serial In - Serial Out Shift Registers (2) In order to get the data out of the register, they must be shifted out serially destructive readout, the original data is lost and at the end of the read cycle, all flip-flops are reset to zero

23 Serial In - Serial Out Shift Registers (3) To avoid the loss of data, an arrangement for a non-destructive reading can be done by adding two AND gates, an OR gate and an inverter to the system. The data is loaded to the register when the control line is HIGH (ie WRITE). The data can be shifted out of the register when the control line is LOW (ie READ).

24 Serial In - Parallel Out Shift Registers Data bits are entered serially Once the data are stored, each bit appears on its respective output line, and all bits are available simultaneously

25 Parallel In - Serial Out Shift Registers The circuit uses D flip-flops and NAND gates for entering data (ie writing) to the register

26 Parallel In - Parallel Out Shift Registers All data bits appear on the parallel outputs immediately following the simultaneous entry of the data bits The following circuit is a four-bit parallel in - parallel out shift register constructed by D flip-flops

27 Bidirectional Shift Registers (1) The registers discussed so far involved only right shift operations Each right shift operation has the effect of successively dividing the binary number by two If the operation is reversed (left shift), this has the effect of multiplying the number by two A bidirectional, or reversible, shift register is one in which the data can be shift either left or right

28 Bidirectional Shift Registers (2) A four-bit bidirectional shift register using D flipflops is shown below

29 Shift Register Counters (Ring Counter) A ring counter is basically a circulating shift register in which the output of the most significant stage is fed back to the input of the least significant stage

30 Shift Register Counters (Johnson Counter) Inverted output of the last stage fed back to the input of the first stage They are also known as twisted ring counters

31 Applications To produce time delay The serial in -serial out shift register can be used as a time delay device. The amount of delay can be controlled by: the number of stages in the register the clock frequency To convert serial data to parallel data Use a serial in - parallel out register