CHAPTER 7

COUNTERS

By Sefneh Getachew
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 Content

 Synchronous (Parallel) Counters

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 Introduction: Counters
 Counters are sequential circuits which count through a specific state sequence.
 They can count up, count down, or count through other fixed sequences.
 A Counter is constructed from two or more flip-flops which change states in a
prescribed sequence.
 Two types of counters:
 synchronous (parallel) counters

 asynchronous (ripple) counters

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 Asynchronous (Ripple) Counters
 The flip-flops do not change states at exactly the same time
 Do not have a common clock pulse.
 The Output of the preceding flip-flop connected to the input
clock of the next flip-flop.
 For ‘n’ flip-flops : we need 2n Asynchronous(ripple) counter.
 Also known as ripple counters, as the input clock pulse
“ripples” through the counter – cumulative delay is a
drawback.
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 Asynchronous (Ripple) Counters…
 Example: 2-bit ripple binary counter.
 Output of one flip-flop is connected to the clock input of the next
more-significant flip-flop.

CLK 1 2 3 4

Q0

Q0 0 1 0 1 0

Q1 0 0 1 1 0

Timing diagram
00  01  10  11  00 ...
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 Asynchronous (Ripple) Counters…
 Example: 3-bit ripple binary counter.
HIGH

J Q0 J Q1 J Q2

CLK C C C
Q0 Q1
K K K

FF0 FF1 FF2

CLK 1 2 3 4 5 6 7 8

Q0 0 1 0 1 0 1 0 1 0

Q1 0 0 1 1 0 0 1 1 0

Q2 0 0 0 0 1 1 1 1 0

Recycles back to 0
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 Asynchronous (Ripple) Counters…
 Example: 4-bit ripple binary counter (negative-edge triggered).

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 Asynchronous Down Counters
 Down counters, count downward from a maximum value to zero,
and repeat.
 Example: A 3-bit binary down counter.

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Q0 Q1 Q2
J Q J Q J Q
C
3-bit binary up counter
CLK C C
Q' K Q' K Q'
K

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Q0 Q1 Q2
J J J
Q Q Q 3-bit binary down counter
CLK C C C
K
Q' K Q' K Q'
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Asynchronous Down Counters…
 Example: A 3-bit binary (MOD-8) down counter.
000
001 111
1
Q0 Q1 Q2
J Q J Q J Q 010 110
CLK C C C
K
Q' K Q' K Q'
011 101
100

CLK 1 2 3 4 5 6 7 8

Q0 0 1 0 1 0 1 0 1 0

Q1 0 1 1 0 0 1 1 0 0

Q2 0 1 1 1 1 0 0 0 0

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 Synchronous (Parallel) Counters
 Apply the same clock pulse to all flip-flop
 All flip-flops change state at the same time , with no ripple
 The problem with Asynchronous counters is that they suffer from “Propagation
Delay”.
 The result of this synchronization is that all the individual output bits changing state at
exactly the same time in response to the common clock signal with no ripple effect

and therefore, no propagation delay.

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 Synchronous (Parallel) Counters…
 Example: 2-bit synchronous binary counter.

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 Synchronous (Parallel) Counters…
 Example: 4-bit synchronous binary counter.
TA3 = A2 . A1 . A0
TA2 = A1 . A0
TA1 = A0
TA0 = 1

1 A1.A0 A2.A1.A0

A0 J A1 J A2 J A3
J Q Q Q Q
C C C C
K
Q' K Q' K Q' K Q'

CLK

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 Synchronous (Parallel) Counters..

 Example: Synchronous decade/BCD counter

Q0

1 T T Q1 T Q2 T Q3
Q Q Q Q
C C C C
Q' Q' Q' Q'

CLK

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 Up/Down Synchronous Counters

 a bidirectional counter that is capable of counting either up or

 Up/Down = 0  Count downward

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 Up/Down Synchronous Counters…
 Example: A 4-bit up/down synchronous binary counter.
TQ0 = 1
TQ1 = (Q0.Up) + (Q0'.Up' )
TQ2 = ( Q0.Q1.Up ) + (Q0'. Q1'. Up' )

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