Hun_Wie_counter.ppt

7/28/2019 Hun_Wie_counter.ppt

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Counters

In digital logic and computing, a counter is a device

which stores (and sometimes displays) the number of

times a particular event or process has occurred,

often in relationship to a clock signal.


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Counters(Continued)

We examine special types of addition and subtraction

operations, which are used for the purpose of

counting.

We will show how the counter circuits can bedesigned using D flip-flops.


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Electronic counters

In electronics, counters can be implemented quite

easily using register-type circuits such as the flip-

flop, and a wide variety of classifications exist:

1. Asynchronous (ripple) counterchanging state bits

are used as clocks to subsequent state flip-flops

2. Synchronous counterall state bits change under

control of a single clock3. Decade countercounts through ten states per stage


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Electronic counters(continued)

4. Up/down countercounts both up and down, under

command of a control input

5. Ring counterformed by a shift register withfeedback connection in a ring

6. Johnson countera twistedring counter

7. Cascaded counter


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D0 = Q0 XOR Enable D1 = Q1 XOR Q0 & Enable D2 = Q2 XOR Q1 & Q0 & Enable

D3 = Q3 XOR Q2 & Q1 & Q0 & Enable


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2x1 MUX to select input, loading external when to clear, loadinginternal value when to count.


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BCD

In computing and electronic systems, binary-coded decimal (BCD)

(sometimes called natural binary-coded decimal, NBCD) or, in its most

common modern implementation, packed decimal, is an encoding for

decimal numbers in which each digit is represented by its own binary

sequence. Its main virtue is that it allows easy conversion to decimal digits

for printing or display, and allows faster decimal calculations. Its

drawbacks are a small increase in the complexity of circuits needed to

implement mathematical operations. Uncompressed BCD is also arelatively inefficient encodingit occupies more space than a purely

binary representation.

In BCD, a digit is usually represented by four bits which, in general,

represent the decimal digits 0 through 9. Other bit combinations are

sometimes used for a sign or for other indications (e.g., error or overflow). Although uncompressed BCD is not as widely used as it once was,

decimal fixed-point and floating-point are still important and continue to

be used in financial, commercial, and industrial computing.


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BCD: 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001

Basics for BCD

To encode a decimal number using the common BCD

encoding, each decimal digit is stored in a 4-bitnibble:

Decimal: 0 1 2 3 4 5 6 7 8 9

Thus, the BCD encoding for the number 127 would

be:

0001 0010 0111

Whereas the pure binary number would be:0111 1111


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Binary-coded-decimal(BCD) counters


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Consists of two modulo-10 counters, one for each

BCD digit.

It is necessary to reset the four flip-flops after the

count of 9 has been obtained. Thus the Load input to

each stage is equal to 1 when Q3=Q0=1, which

causes 0s to be loaded into the flip-flops at the next

positive edge of the clock signal.

Keeping the Enable signal for BCD1 low at all times

except when BCD0 = 9


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IBM and BCD

IBM used the terms binary-coded decimal and BCD for 6-bit

alphamerics codes that represented numbers, upper-case letters andspecial characters. Some variation of BCD alphamerics was used in

most early IBM computers, including the IBM 1620, IBM 1400

series, and non-Decimal Architecture members of the IBM

700/7000 series.

Today, BCD data is still heavily used in IBM processors anddatabases, such as IBM DB2, mainframes, and Power6. In these

products, the BCD is usually zoned BCD (as in EBCDIC or ASCII),

Packed BCD (two decimal digits per byte), or "pure" BCD

encoding (one decimal digit stored as BCD in the low four bits of

each byte). All of these are used within hardware registers andprocessing units, and in software.


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Ring counters are implemented using shift registers. It is essentially a

circulating shift register connected so that the last flip-flop shifts its

value into the first flip-flop. There is usually only a single 1 circulating

in the register, as long as clock pulses are applied. (Starts 1000->0100-

>0010->0001 repeat)

Ring Counter


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Start control signal, which presets the left-most flip-flop to 1 and

clears the others to 0.


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Johnson Counter

The Johnson counter, also known as the twisted-ring counter,

is exactly the same as the ring counter except that the inverted

output of the last flip-flop is connected to the input of the firstflip-flop.

Lets say, starts from 000, 100, 110, 111, 011 and 001, and the

sequence is repeated so long as there is input pulse.


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As well as counting or rotating data around a continuous loop, ring counters

can also be used to detect or recognize various patterns or number values

within a set of data. By connecting simple logic gates such as the AND or the

OR gates to the outputs of the flip-flops the circuit can be made to detect a set

number or value. Standard 2, 3 or 4-stage Johnson ring counters can also be

used to divide the frequency of the clock signal by varying their feedback

connections and divide-by-3 or divide-by-5 outputs are also available.

ClockPulse No

FFA FFB FFC FFD

0 0 0 0 0

1 1 0 0 02 1 1 0 0

3 1 1 1 0

4 1 1 1 1

5 0 1 1 1

6 0 0 1 17 0 0 0 1

Truth Table for a 4-bit JohnsonRing Counter


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To initialize the operation of the Johnson counter, it is necessary to

reset all flip-flops, as shown in the figure. Observe that neither the

Johnson nor the ring counter will generate the desired counting

sequence if not initialized properly.


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Sources :

Digital Logic ,Stephen Brown

http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cwl3/report.html#bcd

http://people.wallawalla.edu/~curt.nelson/engr354/lecture/brown/chapter7_reg_counters.pdf

http://www.electronics-tutorials.ws


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Questions?

Thank you !

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Hun_Wie_counter.ppt