EKT 124 / 3 DIGITAL ELEKTRONIC 1 CHAPTER 3 Counters

INTRODUCTION One of the common requirement in digital circuits/system is counting, both direction (forward and backward) Digital clocks and watches are everywhere, timers are found in a range of appliances from microwave ovens to VCRs, and counters for other reasons are found in everything from automobiles to test equipment. Although we will see many variations on the basic counter, they are all fundamentally very similar.

INTRODUCTION (cont.) Counters can be implemented quite easily using register-type circuits such as the flip-flop, and a wide variety of classifications exist: Asynchronous (ripple) counter – changing state bits are used as clocks to subsequent state flip-flops Synchronous counter – all state bits change under control of a single clock Decade counter – counts through ten states per stage Up/down counter – counts both up and down, under command of a control input Ring counter – formed by a shift register with feedback connection in a ring Johnson counter – a twisted ring counter Cascaded counter Each is useful for different applications

INTRODUCTION (cont.) A counter – a group of flip-flops connected together to perform counting operations. The number of flip-flops used and the way in which they are connected determine the number of states (modulus). Two broad categories according to the way they are clocked: Asynchronous counter Synchronous counter

A 2-bit asynchronous binary counter. ASYNCHRONOUS COUNTER Don’t have fixed time relationship with each other. Triggering don’t occur at the same time. Don’t have a common clock pulse A 2-bit asynchronous binary counter.

The Timing diagram Notice that : Main clock pulse only applied to FF0. Clock for next FF, taken from previous complemented output ( Q ). All inputs (J, K) are high (Vcc).

The Timing diagram

The Binary State Sequence 1 1 1 1 CLOCK PULSE Q1 Q0 Initially 1 2 3 4 (recycles)

Three-bit asynchronous binary counter and its timing diagram for one cycle.

The Binary State Sequence for a 3-bit Binary Counter CLOCK PULSE Q2 Q1 Q0 Initially 1 2 3 4 5 6 7 8 (recycles)

Four-bit asynchronous binary counter and its timing diagram.

ASYNCHRONOUS DECADE COUNTER The modulus of a counter is the number of unique states that the counter will sequence through. The maximum possible number of states (max modulus) is 2n where n is the number of flip-flops. Counter with ten states are called decade counter. Counter can also be designed to have a number of states in their sequence that is less than the maximum of 2n. The resulting sequence is called truncated sequence. To obtain a truncated sequence it is necessary to force the counter to recycle before going through all of its possible states.

An asynchronously clocked decade counter

SYNCHRONOUS COUNTER OPERATION A 2-bit synchronous binary counter.

The Binary State Sequence 1 1 1 1 CLOCK PULSE Q1 Q0 Initially 1 2 3 4 (recycles)

A 3-bit synchronous binary counter. 1 1 1 1 1 1 1 1 1 1 1 1

The Binary State Sequence for a 3-bit Binary Counter CLOCK PULSE Q2 Q1 Q0 Initially 1 2 3 4 5 6 7 8 (recycles)

A 4-Bit Synchronous BCD Decade Counter.

The Binary State Sequence for BCD Decade Counter CLOCK PULSE Q3 Q2 Q1 Q0 Initially 1 2 3 4 5 6 7 8 9 10 (recycles)

General clocked sequential circuit : DESIGN OF SYNCHRONOUS COUNTERS General clocked sequential circuit :

Steps used in the design of sequential circuit: Specify the counter sequence and draw a state diagram Derive a next-state table from the state diagram Develop a transition table showing the flip-flop inputs required for each transition. *** Transition/Excitation Table will be given. Transfer the J and K states from the transition table to Karnaugh maps. There is a Karnaugh map for each input of each flip-flop. Group the Karnaugh map cells to generate and derive the logic expression for each flip-flop input. Implement the expressions with combinational logic, and combine with the flip-flops to create the counter (construct the counter).

Example: Design a counter for 3-bit Gray code by using J-K Flip-flop. State Diagram 0 1 3 2 6 7 5 4 0 1.……..

2. Next-state table for a 3-bit Gray code counter. Present State Next State Q2 Q1 Q0 1

Transition Table for a J-K flip-flop Output Transitions Flip-flop Inputs QN QN+1 J K  X 1 QN : present state QN+1: next state X: Don’t care

3. Karnaugh maps for present-state J and K inputs.

4. Three-bit Gray code counter

Example: Design a counter with the irregular binary count sequence 1,2,5,7,1,…..as shown in the state diagram. Use J-K flip-flops. 1. State Diagram

2. Next-state table Present State Next State Q2 Q1 Q0 1

Transition Table for a J-K flip-flop Output Transitions Flip-flop Inputs QN QN+1 J K  X 1

3. K-Map

4. The Counter Circuit

Transition/Excitation Table for Flip-flop

Example: State diagram for a 3-bit up/down Gray code counter.

UP/DOWN SYNCHRONOUS COUNTER A basic 3-bit up/down synchronous counter.

Timing Diagram

The 74HC190 up/down synchronous decade counter.

Timing example for a 74HC190.

J and K maps - The UP/DOWN control input, Y, is treated as a fourth variable.

Three-bit up/down Gray code counter

CASCADE COUNTERS Two cascaded counters (all J and K inputs are HIGH).

A modulus-100 counter using two cascaded decade counters.

Three cascaded decade counters forming a divide-by-1000 frequency divider with intermediate divide- by-10 and divide-by-100 outputs.

Example: Determine the overall modulus of the two cascaded counter for (a) and (b) For (a) the overall modulus for the 3 counter configuration is 8 x 12 x 16 = 1536 for (b) the overall modulus for the 4 counter configuration is 10 x 4 x 7 x 5 = 1400

A divide-by-100 counter using two 74LS160 decade counters.

A divide-by-40,000 counter using 74HC161 4-bit binary counters A divide-by-40,000 counter using 74HC161 4-bit binary counters. Note that each of the parallel data inputs is shown in binary order (the right-most bit D0 is the LSB in each counter).

Decoding of state 6 (110). COUNTER DECODING * To determine when the counter is in a certain states in its sequence by using decoders or logic gates. Decoding of state 6 (110).

A 3-bit counter with active-HIGH decoding of count 2 and count 7.

A basic decade (BCD) counter and decoder.

Outputs with glitches from the previous decoder Outputs with glitches from the previous decoder. Glitch widths are exaggerated for illustration and are usually only a few nanoseconds wide.

The basic decade counter and decoder with strobing to eliminate glitches.

Strobed decoder outputs for the circuit

Simplified logic diagram for a 12-hour digital clock.

Logic diagram of typical divide-by-60 counter using 74LS160A synchronous decade counters. Note that the outputs are in binary order (the right-most bit is the LSB).

Logic diagram for hours counter and decoders Logic diagram for hours counter and decoders. Note that on the counter inputs and outputs, the right-most bit is the LSB.

Functional block diagram for parking garage control.

Logic diagram for modulus-100 up/down counter for automobile parking control.

Parallel-to-serial data conversion logic.

Example of parallel-to-serial conversion timing for the previous circuit

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