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2תרגול מונים

Counters

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Edge Triggering Important Issue:

The T Flip-Flop and the JK Flip-Flop 1-1 option are not stable since they are “toggle” operations.

From now all FFs are assumed down edge-triggered: Values are changed not when the clock is up, but at the exact moment the clock goes down – notice the circle notation

Edge Triggering mechanism can be seen in the lecture.

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New Approach To Flip-Flops (1) Formerly, we presented each flip-flop’s

Truth Table, i.e. the output as a function of former state (former output) and the inputs.

000

011

101

110

T 1tQtQ

Former State Input Output

T Flip-FlopExample

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New Approach To Flip-Flops (2) A new Approach: For each former output

and desired output combination, what inputs do we need to transform from current to desired?

This approach is more useful when creating counters.

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New Approach To Flip-Flops (3)

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Flip-Flop Concatenation T Flip-Flop has an interesting Attribute:

T Q T Q1 1

CP

10

10

10

(In red, is the clock down-edge)

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Flip-Flop Concatenation (2) But doesn’t that resemble counting in

binary?000

001

010

011

100

101

110

111

0A1A2A

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Asynchronic Counter So we can use this attribute to create a

simple n-digit binary counter. (shown here with the equivalent 1-1 state JK

Flip-Flop)

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BCD Counter Can we count in a radix which is not ? Yes, we can even create a binary-coded

decimal (BCD) Counter:

n2

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BCD Counter (2) To create it we used the diagram:

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BCD Counter Concatenation If we can count to 10 (exclusive) we can

count to 100, 1000 and so on…

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BCD Counter Two problems:

Developing a custom-made, efficient, asynchronic counter, such as the BCD counter is difficult!

What if we want to create a non-consecutive counter easily?

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Counting Sequence A cyclic sequence of binary numbers. For instance: 0,1,2,4,5,6,0,1,2,4,…

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Synchronic Counter We want to implement a mechanism for

counting in a given counting sequence. We’ll focus independently on each digit

and the changes it undergoes.

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Building A Sync. Counter Algorithm:

Choose a Flip-Flop type to use. To each digit (column), allocate a Flip-flop. For each digit (column) create a truth table in the

following manner: For each state (line) do:

Mark state in current line as Mark state in next line as Determine the desired FF’s inputs by the tables. Those inputs

are actually function results in the truth table. Simplify the truth table and implement the function

)(tQ

)1( tQ

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3-Bit Sync. Counter using T Flip-Flops (2)

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3-Bit Sync. Counter using T Flip-Flops (1)

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3-Bit Sync. Counter using T Flip-Flops (3)

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3-Bit Sync. Counter using T Flip-Flops (3)

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3-Bit Sync. Counter using T Flip-Flops (4)

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Example using JK Flip-Flops (2) Shown for the 0,1,2,4,5,6,0,1,2,4,5,6,… example

We’ll do C as an example.

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Example using JK Flip-Flops (1)

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Example using JK Flip-Flops (3) JC:

KC:

1XX0

1XX0

0

1

00 01 11 10ABC

X1XX

X1XX

0

1

00 01 11 10ABC

BJC

1KC

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Example using JK Flip-Flops (4)