B sc cs i bo-de u-iii counters & registers

Registers & CountersCourse: B.Sc.(CS)

Subject: Basics of Digital Electronics

Unit : 3rd

Sem.:1st

COUNTERS

Why do we need counters?

Counters in digital circuits may used for 3 functions:

Timing: Building a precision digital clock is an

example where a low frequency (10 Hz) clock

cannot be achieved with a crystal oscillator.

Sequencing: Starting of a rocket motor is an

example where the energizing of fuel pumps,

ignition, etc. must follow a critical sequence.

Counting: Measuring the flow of traffic on a road

is an application in which the total number of

vehicles passing a certain point needs be counted.

COUNTERS (continued)

A counter is a register that goes through a sequence

of states.

Counter categories:

1. Ripple counters

2. Synchronous counters

• Ripple counters: The flip- flop’s output transition

triggers other flip- flops.

• Synchronous counters: A common clock triggers

all flip- flops simultaneously rather than one at a time

in succession as in ripple counters.

BINARY RIPPLE COUNTER

A binary ripple counter consists of a series

connection of complementing flip-flops à the output

of each flip-flop is connected to the C input of the

next higher-order flip-flop.



Q0 is complemented with the count pulse. Since Q1

goes from 1 to 0, it triggers Q1 and complements it.

As a result, Q1 goes from 1 0, which in turn

complements Q2 changing it from 0 1. Q2 does not

trigger Q3 because Q2 produces a positive transition.

The flip-flops change one bit at a time in succession

and the signal propagates through the counter in a

ripple fashion from one stage to the next.


PROBLEMS WITH RIPPLE COUNTERS

Asynchronous or ripple counters are arranged in

such a way that the output of one flip flop changes

the state of the next. In a long chain of ripple counter

stages, the last flip flop changes its state

considerably later than the first FF due to

propagation delays in each stage. Problems occur if

this delay is longer than the response time of other

logic elements connected to the circuit.

Synchronous counters overcome the problems

of propagation delay and erroneous intermediate

states. In this type of counter all the FF clock inputs

are wired together, so the transitions of all stages

occur simultaneously.

SYNCHRONOUS COUNTERS

Synchronous counters are different from ripple counters

in that the clock is applied to the inputs of all flip-flops,

which triggers all flip flops at the same time.

If T = 0 or J = K = 0, the flip- flop does not change state.

If T = 1 or J = K = 1, the flip- flop complements.

Suppose for a 4-bit counter A3A2A1A0= 0011, the next

count is 0100.

A0is always complemented.

A1is complemented because the present state of A0 =1.

A2 is complemented because the present state of A1A0

=11.

A3 is not complemented because the present state of

A2A1A0 =011.

4-BIT SYNCHRONOUS COUNTER

If the enable is 0 and, all J and K inputs are 0

and the clock does not change the state of

counter.

The first stage A has its J and K = 1 if enable = 1.

The other J and K are equal to 1 if all previous 0

least significant stages are equal to 1. The chain

of AND gates generates the required logic for the

J and K inputs in each stage.

Note that Synchronous counters have a regular

pattern.

4-BIT SYNCHRONOUS COUNTER

Registers & Counters

A register consists of a group of flip- flops and gates

that affect their transition. An n-bit register consists

of n-bit flip-flops capable of storing n bits of binary

information.

In addition to flip- flops, a register may have

combinational gates that perform certain data

processing tasks.

A counter is essentially a register that goes through

a pre-determined sequence of states. The gates in

the counter are connected in such a way to produce

the prescribed sequence of states.


A binary ripple counter consists of a series

connection of complementing flip-flops à the

output of each flip-flop is connected to the C

input of the next higher-order flip-flop.

4-Bit Register

The common clock input triggers all flip- flops on

the positive edge of each pulse à the binary data

available at the 4 inputs are transferred into the

register.

The four outputs can be sampled to obtain the

binary information stored in the register.

When the clear input R goes to zero, all flip- flops

are reset (register is cleared to 0’s)

Fig. 4 Bit Register

Register with Parallel Load

When load input = 1 à data transferred into

register with next clock edge.

When load input = 0 à outputs of Flip-Flops are

connected to their inputs.

Fig: 4 Bit register with parallel load

Shift Registers

A Shift Register is a register that is capable of

shifting its binary information in one or both

directions.

On the leading edge of the first clock pulse, the

signal on the data in is latched in the first flip-

flop. On the leading edge of the next clock pulse,

the contents of the first flip- flop is stored in the

second flip- flop, and the signal which is present

at the data in is stored is the first flip- flop, etc.

Serial Shift Registers – Timing Diagram

Serial Transfer

prevents

loss

of

information

determines when

and how many

times the registers

are shifted.

Each rising edge

of pulse causes a

shift in both

registers

Serial Transfer Example 1

Serial Transfer Example 1 (continued)

With the first pulse T1, (a) the rightmost bit of A is

shifted into the leftmost bit of B and (b) also

circulated into the leftmost position of A.

At the same time, (c) all bits of A and B are shifted

one position to the right.

Serial/Parallel Computation

Communication between a computer and a

peripheral device is usually done serially, while

computation in the computer itself is usually

performed with parallel logic circuitry.

Computations in the computer are done in

parallel because this is a faster mode. Serial

operations are slower but require less devices.

Fig: 4 Bit Adder with Carry Look ahead & 4

Bit Adder- Subtractor.

Serial Addition

Initially, Reg. A holds the augend (# to which another

# is added), B holds the addend (the # that is

added). Shift control enables both Reg.’s, and carry

FlipFlop, so that at the next, both Reg.’s are shifted

once to the right, the sum bit from S enters the

leftmost Flip-Flop of A, a new carry is transferred to

Q, and both registers are shifted once to the right.

Thus, the sumis transferred one at a time into Reg.

A.

Fig: Serial Adder

Parallel Adder vs. Serial Adder

Parallel Adder vs. Serial Adder

1. Parallel adder uses parallel loading, whereas

the serial adder uses shift registers.

2. Number of full adder circuit in the parallel

adder is equal to the number of bits in the binary

numbers. Serial adder requires only one full

adder and a carry Flip -Flop.

3. The parallel adder is a combinational circuit,

whereas the serial adder is a sequential circuit

that consists of a full adder and a Flip-Flop.

Universal Shift Register

A universal shift register is a bidirectional shift

register with parallel load capabilities.



• When S1S0 = 11, the binary information on the parallel input lines is transferred into the register simultaneously at the next clock edge.

• When S1S0= 00, the present value of the register is applied to the D inputs of the FFs. This forms a conduction path from the output to the input of each FF.

• When S1S0= 01, terminal 1 of the multiplexer inputs has a path to the D inputs of the FFs, which causes a shift-right operation, with serial input transferred into FF A3.

• When S1S0= 10, a shift-left operation results with serial input going into FF A0.


Parallel vs. Serial Data Transmission

Shift registers are often used to interface digital

systems situated remotely from each other.

Task: We want to transmit an n-bit quantity between

two location that are far from each other.

What are the options?

1. Use n lines to transmit n bits in parallel. Problem:

Cost is expensive.

2. Use a single line to transmit the information

serially, one bit at a time.

Cost is less.

References

Digital Logic and Computer Design – M. Morris Mano

– Pearson

Fundamentals of Digital Circuits – A. Anand Kumar -

PHI

Digital Electronics - Gothmen - PHI

Digital Electronics Principles - Malvino & Leech -

MGH

Digital fundamentals - Thomes L.Floyd and Jain -

Pearson

Modern Digital Electronics - R.P. Jain - TMH

Web References

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http://www.faadooengineers.com/threads/346-

Digital-Electronics-Lecture-notes-and-study-material

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/gate/material/2.pdf

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B sc cs i bo-de u-iii counters & registers