Three Other Types of
Counters (BCD Counter,
Ring Counter, Johnson
Counter)
Hun Wie (Theo)
SJSU, 2011 Spring
Prof: Dr. Sin-Min Lee
CS147 Computer Organization and Architecture
 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.
 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 be
designed using D flip-flops.
 Electronic
•
counters
In electronics, counters can be implemented quite
easily using register-type circuits such as the flipflop, and a wide variety of classifications exist:
1. Asynchronous (ripple) counter – changing state bits
are used as clocks to subsequent state flip-flops
2. Synchronous counter – all state bits change under
control of a single clock
3. Decade counter – counts through ten states per stage
 Electronic
counters(continued)
4. Up/down counter – counts both up and down, under
command of a control input
5. Ring counter – formed by a shift register with
feedback connection in a ring
6. Johnson counter – a twisted ring counter
7. Cascaded counter




D0
D1
D2
D3
=
=
=
=
Q0
Q1
Q2
Q3
XOR
XOR
XOR
XOR
Enable
Q0 & Enable
Q1 & Q0 & Enable
Q2 & Q1 & Q0 & Enable
2x1 MUX to select input, loading external when to clear, loading
internal value when to count.




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 a
relatively inefficient encoding—it 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.
•
•
•
•
•
Basics for BCD
To encode a decimal number using the common BCD
encoding, each decimal digit is stored in a 4-bit
nibble:
Decimal: 0 1
2 3
4
5 6 7
8
9
BCD: 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001
Thus, the BCD encoding for the number 127 would
be:
0001 0010 0111
Whereas the pure binary number would be:
0111 1111
 Binary-coded-decimal(BCD)
counters
•
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
 IBM
and BCD
• IBM used the terms binary-coded decimal and BCD for 6-bit
alphamerics codes that represented numbers, upper-case letters and
special 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 and
databases, 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 and
processing units, and in software.
 Ring
Counter
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)
Start control signal, which presets the left-most flip-flop to 1 and
clears the others to 0.
 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 first
flip-flop.
Let’s say, starts from 000, 100, 110, 111, 011 and 001, and the
sequence is repeated so long as there is input pulse.
Truth Table for a 4-bit Johnson
Ring Counter
Clock
Pulse No
0
1
2
3
4
5
6
7
FFA FFB FFC FFD
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
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.
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.
 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_co
unters.pdf
•
http://www.electronics-tutorials.ws
Questions?
Thank you !