Digital Design

Rabie A. Ramadan

Lecture 3

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Registers and Counters

Registers

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A circuit with flip-flops is considered a sequential circuit even in the absence of combinational logic.

Register – is a group of flip-flops. Its basic function is to hold information within a digital system so as to make it available to the logic units during the computing process.

However,• A register may also have additional capabilities associated with it.

Counters

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Counter –

• is essentially a register that goes through a predetermined sequence of states.

The gates in the counter are connected in such a way as to produce the prescribed sequence of binary states.

4-bit Register

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Clear will reset all of the FFs

Register with Parallel Load

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If all the bits in a register are loaded at the same time, the loading is done in parallel.

LD Q(t+1)

0 Q(t)

1 D3-D0

The feedback connectionfrom output to input is

necessary because the Dflip-flop does not have a “no

change” condition.

Shift Registers

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Registers capable of shifting their binary contents in one or both directions.

Q0(t+1) = SIQ1(t+1) = Q0(t)Q2(t+1) = Q1(t)Q3(t+1) = Q2(t)

Each clock pulse shifts the contents of the registerone bit position to the right.

Serial Transfer

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Serial transfer of information from register A to register B is done with shift registers:

Assume that the binary content of A before the shift is 1011 and that of B is 0010. The serial transfer occurs in four steps as shown in the table below:

Serial Addition

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Bits in the two registers are added one pair at a time through a single full adder (FA) circuit.

The carry out of the FA is transferred to a D flip-flop.

The output of this flip-flop is then used as the carry input for the next pair of significant bits.

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Counters

Introducing counters

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Counters are a specific type of sequential circuit. The state, or the flip-flop values themselves, serves as the “output.” The output value increases by one on each clock cycle. After the largest value, the output “wraps around” back to 0. Using two bits, we’d get something like this:

Present State Next State A B A B

0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0

00 01

1011

1

11

1

We’ll soon look at some extensions to this basic idea.

What good are counters?

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Counters can act as simple clocks to keep track of “time.” You may need to record how many times something has happened.

• How many bits have been sent or received?

• How many steps have been performed in some computation? All processors contain a program counter, or PC.

• Programs consist of a list of instructions that are to be executed one after another (for the most part).

• The PC keeps track of the instruction currently being executed.

• The PC increments once on each clock cycle, and the next program instruction is then executed.

A slightly fancier counter

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Let’s try to design a slightly different two-bit counter:

• Again, the counter outputs will be 00, 01, 10 and 11.

• Now, there is a single input, X. When X=0, the counter value should increment on each clock cycle. But when X=1, the value should decrement on successive cycles.

We’ll need two flip-flops again. Here are the four possible states:

00 01

1011

The complete state diagram and table

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• Here’s the complete state diagram and state table for this circuit.

– Make sure you know how to come up with these – this is a typical sequential design problem!

00 01

1011

0

0

0

10 1

1

1

Present State I nputs Next StateQ1 Q0 X Q1 Q0

0 0 0 0 10 0 1 1 10 1 0 1 00 1 1 0 01 0 0 1 11 0 1 0 11 1 0 0 01 1 1 1 0

D flip-flop inputs

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If we use D flip-flops, then the D inputs will just be the same as the desired next states.

Present State I nputs Next StateQ1 Q0 X Q1 Q0

0 0 0 0 10 0 1 1 10 1 0 1 00 1 1 0 01 0 0 1 11 0 1 0 11 1 0 0 01 1 1 1 0

D1 =??

D0 =??

D flip-flop inputs

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If we use D flip-flops, then the D inputs will just be the same as the desired next states.

Equations for the D flip-flop inputs are shown at the right.

Present State I nputs Next StateQ1 Q0 X Q1 Q0

0 0 0 0 10 0 1 1 10 1 0 1 00 1 1 0 01 0 0 1 11 0 1 0 11 1 0 0 01 1 1 1 0

D1 = Q1 Q0 X

D0 = Q0’

Circuit

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Here are some D Flip Flop devices They have both normal and

complemented outputs, so we can access Q0’ directly without using an inverter. (Q1’ is not needed in this example.)

This circuit counts normally when Reset = 1. But when Reset is 0, the flip-flop outputs are cleared to 00 immediately.

Standard Counters

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Ripple Counters

• The FF output serves as a trigger to other FFs

Synchronous Counters

• The trigger (Clock ) is common to all FFs

1

clock

Q1 Q21

Binary Ripple Counter

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Negative edge FFs Least significant FF (e.g. A0)

output is an input to the next

one .

Logic -1 is an input

The least significant FF toggles

the output with each clock

Binary Ripple Counter

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Part of the output Simply, A1 will toggle its state when A0

output changes from 1 to 0

A2 toggles its state when A1 output changes from 1 to 0

A3 toggles its state when A2 output changes from 1 to 0

A0 A1 A2 A3

0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1

0 1 0 0

0 1 0 1

0 1 1 0

0 1 1 1

1 0 0 0

. . . .

Another Ripple Counter

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BCD Ripple Counter

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Counts to 9 and back to 0 again

How many FFs required ?• 4

BCD Ripple Counter

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Q1 triggers Q2 and Q8

Q2 triggers Q4

Q2 and Q4 inputs to J in Q8

Synchronous counters

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Clock is common to all FFs

Change in all FFs done at the same time

Change decision is based on the input circuits

Binary Counters

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Up-Down Binary Counter

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Up/Down Counter can either count up or down on each clock cycle

Up counter counts from 0000 to 1111 and then changes back to 0000

Down counter counts from 1111 to 0000 and then back to 1111

Counter counts up or down each clock cycle

Output changes occur on clock rising edge

Counters with Parallel Load

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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

Summary

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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