Authors: Mircea R. Stan, Alexandre F. Tenca and Milos D. Ercegovac - PowerPoint PPT Presentation

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Authors: Mircea R. Stan, Alexandre F. Tenca and Milos D. Ercegovac

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1. Authors: Mircea R. Stan, Alexandre F. Tenca and Milos D. Ercegovac ... Counter is a special type of adder in which one operand is kept constant. ... – PowerPoint PPT presentation

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Title: Authors: Mircea R. Stan, Alexandre F. Tenca and Milos D. Ercegovac


1
Long and Fast Up/Down Counters
Authors Mircea R. Stan, Alexandre F. Tenca and
Milos D. Ercegovac
Reader Pushpinder Kaur Chouhan
2
Long and Fast Up/Down Counters
  • Introduction
  • Basic Counters
  • Counters Classification
  • Prescaled Counters
  • Constant-Time Up/down Counters
  • Alternative Design
  • Conclusion
  • References

3
Long and Fast Up/Down Counters
  • Introduction
  • Definition of counter
  • What is the article about
  • Basic Counters
  • Counters Classification
  • Prescaled Counters
  • Constant-Time Up/down Counters
  • Alternative Design
  • Conclusion
  • References

4
Introduction
  • Counter is a special type of adder in which one
    operand is kept constant.
  • Mod number number of states 2n in a counter (n
    is number of flip-flops)
  • Generally counter can be written as Binary modulo
    2n n-bit counter, where the value s(t) of the
    counter is incremented by one in each clock
    cycle

  • s(t1) s(t) mod 2n

In Out Up/Down Load CNT Reset
CLK TC
N
N
Black-box generic counter model with the most
common control signals
5
Introduction
  • Problem- When the up/down counter changes
    direction from counting up to counting down or
    vise versa.
  • Solution-
  • use Shadow register for storing the previous
    counter state.
  • restore the previous state in constant time, by
    storing the carry bits in a Carry/Borrow
    register.

6
Long and Fast Up/Down Counters
  • Introduction
  • Basic Counters
  • Asynchronous Counter
  • Synchronous Counter
  • Synchronous Decade Counter
  • Ring Counter
  • Twisted-ring Counter
  • Counters Classification
  • Prescaled Counters
  • Constant-Time Up/down Counters
  • Alternative Design
  • Conclusion
  • References

7
Basic Counters
  • Asynchronous Counter

8
Basic Counters
  • Asynchronous up/down Counter

Sequence Table -
9
Basic Counters
  • Synchronous Counter

Synchronous up/down Counter
10
Basic Counters
Asynchronous Decade Counter
11
Basic Counters
  • Ring Counter

D Q3 CLK Q3
D Q2 CLK Q2
D Q1 CLK Q1
D Q0 CLK Q0
Q3
Q2
Q1
Q0
1000 0100 0010 0001
12
Basic Counters
  • Twisted-ring Counter

D Q2 CLK Q2
D Q1 CLK Q1
D Q0 CLK Q0
Q2
Q1
Q0
000 100 110 111
011 001
13
Long and Fast Up/Down Counters
  • Introduction
  • Basic Counters
  • Counters Classification
  • Based on initialization of the state
  • Based on counting sequence
  • Based on the way of supplying the clock signal
  • Based on the state diagram
  • Based on the number of states
  • Based on the state encoding
  • Prescaled Counters
  • Constant-Time Up/down Counters
  • Alternative Design
  • Conclusion
  • References

14
Counters Classification
  • Based on initialization of the state
  • Noninitalizable
  • Resettable
  • Loadable
  • Based on counting sequence
  • Up-only
  • Down-only
  • Up/down
  • Based on the way of supplying the clock signal
  • Asynchronous
  • Semisynchronous
  • Synchronous
  • Based on the state diagram
  • Periodic
  • Aperiodic

15
Counters Classification
  • Based on initialization of the state
  • Based on counting sequence
  • Based on the way of supplying the clock signal
  • Based on the state diagram
  • Based on the number of states
  • Modulo-2N
  • Modulo-P
  • Based on the state encoding
  • Binary
  • Quasi-Binary
  • Non-Binary

16
Long and Fast Up/Down Counters
  • Introduction
  • Basic Counters
  • Counters Classification
  • Prescaled Counters
  • Characteristics
  • Basic idea
  • Block Diagram
  • Partitioning
  • Constant-Time Up/down Counters
  • Alternative Design
  • Conclusion

17
Prescaled Counter
  • Characteristics
  • Binary counting sequence
  • Clock period independent of counter size
  • Readable on the fly
  • Space complexity linear in the number of bits
    i.e., (O(N))
  • Count up, down, or up/down
  • Resettable

18
Prescaled Counter
  • Basic Idea Characteristic of binary number
    system. i.e., The higher order bits are stable
    for long periods of time and the terminal count
    (TC) output from the two least significant bits,
    which becomes a CARRY-in into the most
    significant block, is periodic with a lower
    frequency than the clock signal.

Binary Sequence Counting Up
19
Prescaled Counter
Prescaling long counters requires partitioning
them into a series of sub-blocks of increasing
sizes in order to take advantage of the reduced
frequency required by high order bits.
20
Prescaled Counter
  • Partitioning methods -
  • Top-down manner First determine the size of
    most significant block, which is chosen as large
    as possible and then recursively determine the
    size of the lower order blocks. N-bit counter is
    first partitioned into an (N - log2N ) most
    significant block and into another log2N block.
    Eg- 64-bit counter is partitioned in block sizes
    58, 3, 2, 1 and 128-bit counter in 121, 4, 2, 1.
  • Bottom-up manner - First determine the size of
    least significant block, then choose the second
    block as large as possible and then the third and
    so on. Least significant block with n0 1-bit
    the second block with n1 2 to the power n0
    2-bits and the third block with n2 2 the power
    (n0 n1) 8 bits and so on. Eg- 64-bit
    counter is partitioned in block sizes 51, 8, 2, 1
    and 128-bit counter in 117, 8, 2, 1.

21
Long and Fast Up/Down Counters
  • Introduction
  • Basic Counters
  • Counters Classification
  • Prescaled Counters
  • Constant-Time Up/down Counters
  • Main idea
  • Block Diagram
  • Least-Significant Bit Counter
  • Configuration Bit
  • Clock Period
  • Up/Down Ring Counter
  • Partitioning
  • Incrementer/Decrementer
  • Alternative Design
  • Conclusion

22
Constant-Time Up/down Counters
  • Main idea - Store the previous block value in
    the Shadow register whenever the block is loaded
    with a new value and simply load this value when
    necessary, instead of trying to compute it.
  • Issues that determine the structure of the new
    counter
  • The prescaled TC generation must itself be
    up/down, for that up/down ring counter is used.
  • Each block needs to be configurable for counting
    either up or down. A separate configuration bit
    for each block is needed to keep track of the
    block configuration.
  • Each sub-block has a shadow register that stores
    the previous block value. When the block
    configuration is up, the shadow register stores
    the present value minus one LSB and when the
    configuration is down, it stores the present
    value plus one LSB.

23
Constant-Time Up/down Counters
24
Partitioning
  • Determining the partition sizes for the
    proposed up/down counter proceeds top-down, the
    minimum clock period (Tclk) is larger than the
    combinational unit delay due to the extra
    complexity. If we consider Tclk pd, where d is
    the unit delay, the partitioning first divides
    the N-bit counter into a most significant N -
    (log2 N/P) block and into another (log2 N/P)
    block which is recursively divided in the same
    manner until the smaller block is a 1-bit
    counter.
  • Example For p 4 and N 64, the
    partitioning leads to the sizes 60, 3, 1.

25
Up/Down Ring Counter
  • The ring counter inside each block is used to
    generate the TC in constant time for the block.
  • When counting up, TC1 when the state of the
    enable counter is s(t)10000
  • When counting down, TC1 when the state of the
    enable counter is s(t)00000

26
Incrementer/decrementer
Incrementer/decrementer can be easily implemented
as a ripple carry chain. For an n-bit block, the
delay through the ripple chain will be n times
the unit logic delay.
27
Least-Significant Bit Counter
  • A 1- bit counter counts in the same sequence, so
    it does not effect whether it count up or
    down.
  • It act as both 1-bit least significant bit and
    as a ring counter for the second block.
  • There is no need for a shadow register or
    configuration bit for the first block.

28
Configuration Bit
  • A configuration bit for each higher order block
    keeps track of how the block is configured
    (up/down). There are four cases
  • Block is configured up and a carry-in comes from
    ring counter.
  • Block is configured down and a borrow-in comes
    from ring counter.
  • Block is configured up and a borrow-in comes
    from ring counter.
  • Block is configured down and a carry-in comes
    from ring counter.

29
Example- 64bit ( 60,3,1)
30
Constant-Time Up/down Counters
31
Long and Fast Up/Down Counters
  • Introduction
  • Basic Counters
  • Counters Classification
  • Prescaled Counters
  • Constant-Time Up/down Counters
  • Alternative Design
  • Use of Carry/Borrow Register
  • Conclusion
  • Comment
  • References

32
Alternative Design
  • Store the bit-wise XOR between the previous
    state and the current state in a Carry/Borrow
    register. With this information available, it is
    possible to restore the desired previous state in
    one gate delay.

33
Long and Fast Up/Down Counters
  • Introduction
  • Basic Counters
  • Counters Classification
  • Prescaled Counters
  • Constant-Time Up/down Counters
  • Alternative Design
  • Conclusion
  • Comment
  • References

34
Conclusion
  • Use Shadow register to store the previous value
    of the counter and just swap the value when
    counter change the direction.
  • Use the Carry/Borrow register to store the
    bit-wise XOR between the previous state and
    current state.
  • Use of shadow register is better than the
    carry/borrow register, as CBreg restore the value
    in one gate delay.

35
Long and Fast Up/Down Counters
  • Introduction
  • Basic Counters
  • Counters Classification
  • Prescaled Counters
  • Constant-Time Up/down Counters
  • Alternative Design
  • Conclusion
  • Comment
  • References

36
Comment
  • Use twisted-ring counter instead of ring counter
    in constant up/down counter with shadow register
    will be fast and may use less clock period.
  • Mod-N Twisted-ring counter can be constructed by
    connecting N/2 flip-flops, where as in Mod-N ring
    counter N flip-flops are required.
  • We can use Bottom-up manner partitioning, as in
    top-down manner partitioning the counters of
    different sizes will require different partition
    sizes.
  • The state bits in the twisted-ring counter are
    such that the s(t)(1000) state can be detected
    by the two most significant bits and the
    s(t)(0000) state can be detected by testing the
    most and least significant bits.

37
Up/Down Twisted-ring Counter
000 100 110 111
011 001
38
Long and Fast Up/Down Counters
  • Introduction
  • Basic Counters
  • Counters Classification
  • Prescaled Counters
  • Constant-Time Up/down Counters
  • Alternative Design
  • Conclusion
  • Comment
  • References

39
References
  • Digital Systems Principles and Application By
    Ronald J. Tocci.
  • Computer Arithmetic Algorithms and Hardware
    Designs By Behrooz Parhami
  • http//www.play-hookey.com/digital/synchronous
    counter.html
  • http//www.eelab.usyd.edu.au/digital_tutorial/part
    2/counter01.html
  • http//www.hcc.hawaii.edu/richardi/113/index.htm

40
Questions ?
41
Basic Counters
Synchronous Decade Counter
  • Q0 toggles on each clock pulse.
  • Q1 changes on the next clock pulse each time
    Q01 and Q30.
  • Q2 changes on the next clock pulse each time
    Q0Q11.
  • Q3 changes on the next clock pulse each time
    Q01, Q11 and Q21 (count 7), or when Q01 and
    Q31 (count 9).

42
Basic Counters
Differential Counter -
? k (d1-d2)
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