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7/28/2019 Lecture 2 - Combinational and Sequential Logic
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1Digital Electronics EEE3017WR. Verrinder (2008)
Announcements
Laboratories and Tutorials will be held at the following times:
Monday (15h00 17h00)
Tuesday (15h00 17h00)
Venue Change: Laboratory 1 will be held in the White Lab
Tutorials will be handed out during the tut session and must be
completed and handed in by your next lecture (Thursday Lectures)
It is a DP requirement to attend at least 50% of all labs and tutorials
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2Digital Electronics EEE3017WR. Verrinder (2008)
Textbooks
There is no set textbook for this course, however, these
books maybe useful for certain sections of work:
Logic and Computer Fundamentals (Mano & Kine)
The Art of Electronics (Horowitz & Hill)
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3Digital Electronics EEE3017WR. Verrinder (2008)
Digital Circuits
There are two main
classes of digital
circuits:
Combinational Circuits
Sequential Circuits
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4Digital Electronics EEE3017WR. Verrinder (2008)
Combinational Circuits
Have no memory
Output only depends on the inputs
To reverse engineer the circuit:
Cycle through all the inputs and note the outputs for
each input
INPUT OUTPUT1 2 3
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5Digital Electronics EEE3017WR. Verrinder (2008)
Sequential Circuits
Have memory
Output is a function of inputs and the state of
the circuit
Cannot just use inputs and outputs to determinethe circuits construction
OUTPUTINPUT
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6Digital Electronics EEE3017WR. Verrinder (2008)
Off the Shelf Digital Chips
Some digital functions
are so useful that they
have dedicated chips
This include: Multiplexers
Decoders
Adders
Flip-flops
Counters etc.
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7Digital Electronics EEE3017WR. Verrinder (2008)
Multiplexers
Are selector devices Take multiple inputs and
output one signal based on
the value of the select
signals
Have:
n inputs
1 output log2n selection lines
Examples: 74HC157; 74HC153;
74HC356
Sel1 Sel2 Output
0 0 In0
0 1 In1
1 0 In2
1 1 In3
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8Digital Electronics EEE3017WR. Verrinder (2008)
Multiplexers cont.
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9Digital Electronics EEE3017WR. Verrinder (2008)
Encoder
Converts a signal into
a specific code
Used for:
Encrypting data
Data compression
Translating one code
to another
In3 In2 In1 In0 Out1 Out0
0 0 0 1 0 00 0 1 0 0 1
0 1 0 0 1 0
1 0 0 0 1 1
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11Digital Electronics EEE3017WR. Verrinder (2008)
Addition Circuits Half Adder
Adds 2 bits together
A
+ BSum
Sum: AB Carry: A.B
Problem!
0
001
0
1
1
1Carry1
1
0
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12Digital Electronics EEE3017WR. Verrinder (2008)
Problem!
Adds two bits together but cant handle an
input carry bit
This is why it is called a half adder
SolutionFULL ADDER
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13Digital Electronics EEE3017WR. Verrinder (2008)
Addition Circuits Full Adder
Has 3 inputs:
Input A
Input B
Carry In
2 outputs
Sum
Carry Out
Made by combining 2 half
adders and an OR gate
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14Digital Electronics EEE3017WR. Verrinder (2008)
Multi-bit Wide Adder
To make multi-bit wide adders:
Cascade a number of full adders
The carry out bits are fed into the carry in bits
etc.
Problems with this approach:
Cascading circuits leads to poor overall circuit
performance
Chips not infinitely fast
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15Digital Electronics EEE3017WR. Verrinder (2008)
RS Flip-flops
Have memory
Made by cross-coupling
two:
NAND gates
NOR gates
Pull LOW and Q goes
HIGH and stays HIGH
until pulled LOW
S
R
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16Digital Electronics EEE3017WR. Verrinder (2008)
D-type Flip-Flops
Have following inputs: D Clock (CLK)
S
R
Have following outputs Q Q
On clock edge, the value
on D is transferred to Qand stays there
R and S are used to putdevice into known state
D CLK Next State of Q
X 0 No Change
0 h 01 h 1
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17Digital Electronics EEE3017WR. Verrinder (2008)
JK Flip-flops
Operation similar to D-type except has twoinputs J and K
When J is HIGH, flip-flopis SET
When K is HIGH, flip-flopis RESET
If both J and K are high,output simply TOGGLES
J K Next State of Q
0 0 No change
0 1 0
1 0 1
1 1 Toggle
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18Digital Electronics EEE3017WR. Verrinder (2008)
Counters
Go through a set sequence of states when pulsesare applied to the input
Different types:
Ripple counters
Synchronous counters
Johnson counters
Decade counters.
Up-down counters Ring counters
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19Digital Electronics EEE3017WR. Verrinder (2008)
Ripple Counter
Made using flip-flops which can complement their
outputs
2nd flip-flop only toggles when first flip-flop has changed
state
Outputs do not all change at the same time
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20Digital Electronics EEE3017WR. Verrinder (2008)
Shift Registers
Data is put in load input
For every clock pulse, data is shifted 1 bit to the right
Used to implement: Parallel to serial conversion
Used often in microprocessors
Serial to parallel conversion
101
10 0 01 1
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21Digital Electronics EEE3017WR. Verrinder (2008)
Design of Sequential Circuits
using D-type Flip-flops D-type flip-flops used to hold systems current state
Use combinational logic to make system move from
state to state
Flip flops holdCURRENT
state
Combinational
circuit calculates
NEXTstate
Combinational
logic calculates
OUTPUTS for
each state
D inputs
System
Inputs
Q
Outputs SystemOutputs
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22Digital Electronics EEE3017WR. Verrinder (2008)
How to Design the
Combinational Circuit
Draw a present state
next state diagram
Show:
Inputs
Present States
Next States
Enter values in next
state column given
inputs and current state
Simplify using standard
logic reduction tools
Input
Present
1
(Q1)
Present
0
(Q0)
Next
1
(D1)
Next
0
(D0)
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
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24Digital Electronics EEE3017WR. Verrinder (2008)
Example 1 - Solution
Firstly there are no external inputs
Use two D-type flip flops as
This gives us 4 possible states. This is fine as we just use dont care
conditions for the unwanted state
To create the combinational logic use aPresent state Next State Diagram
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25Digital Electronics EEE3017WR. Verrinder (2008)
Example 1 Solution cont.
Present Next
(Q1) (Q0) (D1) (D0)
0 0
0 1
1 0
1 1
D1 = Q0 Need to use a
Karnaugh Map to
find D00 0
0 1
01
X X
Count Sequence:
0-1-2-repeat
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26Digital Electronics EEE3017WR. Verrinder (2008)
Example 1 Solution cont.
)QQ(
QQD
10
100
0 1
0
1
Q0
Q1
1
X
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