# Sequential Circuits-2 Study Notes for EE/EC

By BYJU'S Exam Prep

Updated on: September 25th, 2023

In this article, you will find the Study Notes on Sequential Circuits-2 which will cover the topics such as Registers, Counters, Classification of counters, Asynchronous and Synchronous Counters, FSMs.

Table of content

## Registers

When a group of the flip flop is used to store a word ( a group of bits) then it is called a register. To store n bits, n flip flops are cascaded in the register. If in a register, the binary information can be moved from stage to stage, this type of register is called a shift register. According to data movement in a register, shift registers can be classified as

• Serial Input Serial Output (SISO)
• Serial Input Parallel Output (SIPO)
• Parallel Input Serial Output (PISO)
• Parallel Input Parallel Output (PIPO)

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Serial Input Serial Output (SISO)

• In registers edge, trigger circuit is used to make the circuit synchronous.
• If no clock is applied then get the same data which is stored.
• In N bits SISO registers to provide N bits data, Serially in require an N clock pulse, and Serially out require an (N-1) clock pulse.

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Serial Input Parallel Output (SIPO)

• To provide N-bit data: Serial in requires an N clock pulse, and Parallel out requires no clock pulse.
• SIPO can provide n × tCIK delay to the input.
• SIPO can convert serial data or temporal code to parallel or serial code.

## Parallel Input Serial Output (PISO)

• If control = 0 then it acts as parallel input;
• If control = 1 then it acts as serial output;
• To provide parallel input, one clock pulse is required.
• To provide N bits serial output, it requires (N-1) clock pulse.
• PISO can convert special code to temporal code.

Parallel Input Parallel Output (PIPO)

• In PIPO register for parallel input number of pulse required is 1 clock pulse.
• In PIPO register for parallel output number of pulse required is 0 clock pulse.
• PIPO register cannot be used as a shift register.
• It is used for temporal storage of data in microcontroller, DSP, CPU etc.

Summary of Registers

## Counter

• A counter is a sequential logic circuit capable of counting the number of clock pulses arriving at its clock input.
• The sequence of count may be ascending, descending or non-sequence.
• For a counter circuit having n flip flops, Maximum possible states (N) = 2n
• If N = 2n, the counter acts as a binary counter.
• If  N < 2n, the counter is the non-binary counter.
• Its counter is capable to count from 0 to 2n-1.
• The MOD number is the Number of states present in a counter is known as modulus count or MOD number.
• For n-flip flops, the counter will have 2n different states then this counter is said MOD- 2n counter.

## MOD-N Counter

• The MOD number indicates frequency division obtained from the last flip flops.

• MOD-MN counter:
• Overall states of combined counter = MN
• Input frequency = f
• Output frequency f = f/(MN)

## Classification of Counters

Based on the application clock pulse, counters are classified into two categories.

• Synchronous counter
• Asynchronous counter (ripple counter)

## Toggle Mode Circuit

These are frequency divider circuits.

Other Toggle Mode Circuit

## Asynchronous Counter (Ripple counter)

• A different clock pulse is applied to different flip-flops.
• All flip-flops are operating in toggle mode.
• In the asynchronous counter flip flop applied with an external clock acts as an LSB bit.

3-bit Ripple Up Counter

• The input clock is applied at the LSB bit.
• Its n-bit ripple counter maximum possible states are 2n.
• Bit ripple-up counter counts from 0 to 2n – 1.
• If all states are used then with input frequency f, the output frequency will be f/2n
• Calculation of Time Period of Flip Flop: In the n-bit ripple counter if the propagation delay of each flip flop is tpd(FF), then the time period of the clock is:

• Maximum Clock Frequency:

• Due to propagation delays of flip flops decoding errors are present.
• Clear and preset are known as asynchronous input to flip-flop.
• In any ripple counter, the following conditions will fulfil
• Negative edge trigger and Q as clock ⇒ up counter
• Positive edge trigger and Q as clock ⇒ up counter

3-bit Ripple Down Counter

• Positive edge trigger and Q as clock ⇒ down counter
• Negative edge trigger and Q as clock ⇒ down counter

## Non-binary Ripple Counter

A decode counter or BCD counter is an example of a non-binary counter. It requires 4 flip flops.

• Used state = 10 and unused states = 6 → (24 -10)
• Output frequency of BCD counter = f/10
• For making a non-binary counter clear (clr) signal is used.
• c1r is active high, and (clr)’ is active low.

## Synchronous Counters

In this type of counter, there are no connections between the first flip-flop output to the clock input of the next flip-flop.

Ring Counter: It is a circular shift register with only flip flop being set at any particular time, all others are cleared. It is a shift register with feedback.

• In ring counter, if feedback is used the number of states is reduced.
• With n flip flops maximum states = n.
• Number of unused states in ring counter = 2n – n
• Maximum Clock Frequency: If the input frequency is f, then at the output of every flip flop we get f/N frequency. In-ring counter, if the propagation delay of each flip flop is tpd(FF) then

Jhonson Ring Counter: Jhonson ring counter is also called as a Twisted ring counter, Switch tail counter, Creeping counter, or Mobies counter.

• In n – bit Jhonson counter maximum used states = 2n, unused states = 2n – 2n.
• If the input clock frequency is f, the output frequency of each flip flop is f /2n and the duty cycle is 50%.
• A disadvantage of the Jhonson Ring Counter: Lockout may occur. To decode each state one, or two input AND or NOR gate is used.

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