1. Lecture 27 Counters Give qualifications of instructors: DAP
teaching computer architecture at Berkeley since 1977
Co-athor of textbook used in class
Best known for being one of pioneers of RISC
currently author of article on future of microprocessors in SciAm Sept 1995 RY
took 152 as student, TAed 152,instructor in 152
undergrad and grad work at Berkeley
joined NextGen to design fact 80x86 microprocessors
one of architects of UltraSPARC fastest SPARC mper shipping this Fall

2. Counters are important components in computers
Overview
Counters are important components in computers
The increment or decrement by one in response to input
Counters with D Flip Flops
Counters with JK and T Flip Flops
Types of Counters
Ripple counters
Flip flop output serves as a source for triggering other flip flops
Synchronous counters
All flip flops triggered by a clock signal
Synchronous counters are more widely used in industry.
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

3. Counter: A register that goes through a prescribed series of states
Counters
Counter: A register that goes through a prescribed series of states
Binary counter
Counter that follows a binary sequence
N bit binary counter counts in binary from n to 2n-1
Ripple counters triggered by initial Count signal
Applications:
Watches
Clocks
Alarms
Web browser refresh

4. 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.
Proceed through a well-defined sequence of states in response to
count signal
3 Bit Up-counter: 000, 001, 010, 011, 100, 101, 110, 111, 000, ...
3 Bit Down-counter: 111, 110, 101, 100, 011, 010, 001, 000, 111, ...
Binary vs. BCD vs. Gray Code Counters
A counter is a "degenerate" finite state machine/sequential circuit where the state is the only output

5. 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) 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

6. 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

8. Counter Design Procedure

9. Counter Design Procedure

10. Counter Design Procedure
Example Continued

11. Counter Design Procedure
Example Continued
K-maps for Toggle
Inputs:
Resulting Logic Circuit:

13. Binary Ripple Counter Reset signal sets all outputs to 0
Count signal toggles output of low-order flip flop
Low-order flip flop provides trigger for adjacent flip flop
Not all flops change value simultaneously
Lower-order flops change first
Focus on D flip flop implementation
MSI counters come in two categories: ripple counters and synchronous counters.
In a ripple counter, the flip-flop output transition serves as a source for triggering other flip flops

14. Another Asynchronous Ripple Counter
Similar to T flop example on previous slide

15. Asynchronous Counters
Each FF output drives the CLK input of the next FF.
FFs do not change states in exact synchronism with the applied clock pulses.
There is delay between the responses of successive FFs.
Ripple counter due to the way the FFs respond one after another in a kind of rippling effect. A3 A2 1 A1 A0

16. Decade Decimal BCD Counter
A decade counter, since it counts from 0 to 9. To
count in decimal from 0 to 99, we need a two-decade counter.
And
To count from 0 to 999
Three-decade decimal BCD counter

18. Synchronous counters Synchronous(parallel) counters Remember
Synchronous counters are distinguished from ripple counters in that clock pulses are applied to the CP inputs of all flip-flops. The common pulse triggers all the flip-flops
simultaneously, rather than one at a time in succession as in a ripple counter.
Synchronous(parallel) counters
All of the FFs are triggered simultaneously by the clock input pulses.
All FFs change at same time
Remember
If J=K=0, flop maintains value
If J=K=1, flop toggles
Most counters are synchronous in computer systems.
Can also be made from D flops
Value increments on positive edge

19. Synchronous counters Synchronous counters
Same counter as previous slide except Count enable replaced by J=K=1
Note that clock signal is a square wave
Clock fans out to all clock inputs

20. Circuit operation
Count value increments on each negative edge
Note that low-order bit (A) toggles on each clock cycle

21. Synchronous UP/Down counters
Up/Down Counter can either count up or down on each clock cycle
Up counter counts from to 1111 and then changes back to 0000
Down counter counts from to 0000 and then back to 1111
Counter counts up or down each clock cycle
Output changes occur on clock rising edge

22. Counters with Parallel Load
Counters with parallel load can have a preset value
Load signal indicates that data (I3…I0) should be loaded into the counter
Clear resets counter to all zeros
Carry output could be used for higher-order bits

23. Counters with Parallel Load
Clear Clk Load Count Function
X X X Clear to 0
↑ X Load inputs
↑ Count
↑ No Change
Function Table
If Clear is asserted (0), the counter is cleared
If Load is asserted data inputs are loaded
If Count asserted counter value is incremented

24. Binary Counter with Parallel Load and Preset
Presettable parallel counter with asynchronous preset.
If PL’ = 0, load P into flops

25. Binary Counter with Parallel Load and Preset
Commercial version of binary counter

27. 4 Bit Binary Counter with D Flip Flops
D0 = Q0 XOR Enable
D1 = Q1 XOR Q0 & Enable
D2 = Q2 XOR Q1 & Q0 & Enable
D3 = Q3 XOR Q2 & Q1 & Q0 & Enable

28. Binary Counter with Parallel Load
2x1 MUX to select input, loading external when to clear, loading internal value when to count.

29. 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.

30. Basics for BCD
To encode a decimal number using the common BCD encoding, each decimal digit is stored in a 4-bit nibble:
Decimal:
Thus, the BCD encoding for the number 127 would be:
Whereas the pure binary number would be:
BCD:

31. Binary-coded-decimal(BCD) counters

32. 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

33. 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.

34. 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)

36. Start control signal, which presets the left-most flip-flop to 1 and clears the others to 0.

37. 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.

38. Truth Table for a 4-bit Johnson Ring Counter
Clock Pulse No
FFA
FFB
FFC
FFD 1 2 3 4 5 6 7
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.

39. 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.

41. Binary counters can be ripple or synchronous
Summary
Binary counters can be ripple or synchronous
Ripple counters use flip flop outputs as flop triggers
Some delay before all flops settle on a final value
Do no require a clock signal
Synchronous counters are controlled by a clock
All flip flops change at the same time
Up/Down counters can either increment or decrement a stored binary value
Control signal determines if counter counts up or down
Counters with parallel load can be set to a known value before counting begins.
D, T and J/K Flip Flops can be used for counter design
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.