Basic Counters: Part I

Section 7-6 (pp. 353-366)

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Definition• Counter is a register that goes through a

sequence of states as it is clocked• Binary counter ♦ Counts through a binary sequence

•Example: 2 bit “up” counter; a circuit with 2 FFs that goes through the

sequence of states: (00 , 01, 10, 11)2 = (0, 1, 2, 3)10

♦ n bit “up” counter counts from 0 to 2n – 1♦ n bit “down” counter counts from 2n – 1

to 0

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Waveforms of a 2 bit Counter Counter

CP

BA

0 1 2 3 0 1

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Synchronous Counters• Clock inputs of all FFs receive a

common clock pulse

• Change in state is determined from the present state of the counter

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Synchronous Counter

• Count enable, EN = 0♦ counter remains in

the same state• Count enable, EN = 1♦ counter counts up

• Carry output, CO used to expand

counter(e.g. to 8 bits)

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Arbitrary Count• Counter goes through an

arbitrary sequence• Example:

States 3 and 7 are not used

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State Diagram of Example Arbitrary CounterAnalysis of state diagram shows:if circuit ever goes in an unused sate (011 or 111) the next clock transfers it to a valid state ( )AD A B

( )CD B C

BD C

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Circuit of Example Arbitrary Counter

( )AD A B

( )CD B C

BD C