Digital Electronics EEE3017W

1
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

2
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)

3
Digital Circuits

• There are two main classes of digital circuits
• Combinational Circuits
• Sequential Circuits

4
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

1
2
3
5
Sequential Circuits

• Have memory
• Output is a function of inputs and the state of
  the circuit
• Cannot just use inputs and outputs to determine
  the circuits construction

6
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.

7
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

8
Multiplexers cont.
9
Encoder

• Converts a signal into a specific code
• Used for
• Encrypting data
• Data compression
• Translating one code to another

10
Decoders

• Does the reverse of an encoder
• Different types of decoder
• n-to-2n decoder
• 7 segment display decoder
• BCD decoder
• n-to-2n decoders convert binary information from
  n encoded bits to 2n unique outputs
• Examples74HC137 74HC42 74HC139

11
Addition Circuits Half Adder

• Adds 2 bits together
• A
• B
• Sum
• Sum A?B
• Carry A.B
• Problem!

0
1
Carry 1
12
Problem!

• Adds two bits together but cant handle an input
  carry bit
• This is why it is called a half adder
• Solution FULL ADDER

13
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

14
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

15
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

16
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 Q
  and stays there
• R and S are used to put device into known state

17
JK Flip-flops

• Operation similar to D-type except has two inputs
  J and K
• When J is HIGH, flip-flop is SET
• When K is HIGH, flip-flop is RESET
• If both J and K are high, output simply TOGGLES

18
Counters

• Go through a set sequence of states when pulses
  are applied to the input
• Different types
• Ripple counters
• Synchronous counters
• Johnson counters
• Decade counters.
• Up-down counters
• Ring counters

19
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

20
Shift Registers
0
1
1
0
0
1
101

• 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

21
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

22
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

23
Example 1

• Design a counter that counts in the following
  sequence
• 0 1 2 repeat
• The counter must not be a ripple type

24
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 a Present
  state Next State Diagram

25
Example 1 Solution cont.
Count Sequence 0-1-2-repeat

• D1 Q0
• Need to use a Karnaugh Map to find D0

26
Example 1 Solution cont.
Q1
Q0
1
X
27
Example 1 Solution cont.