Registers

1
ECE U322Digital Logic Design
Nov 28th, 2004

• Lecture 31
• Controllers are Finite State Machines
• traffic light controller
• State Machine encoding
• Homework 8 due next Monday Dec 5th

2
Announcements

• Final exam is on Dec. 13, 1030 am, 154 Ryder
  Hall
• New TA Office Hour
• Tuesday, 225 325PM, 232 Forsyth
• Midterm II Statistics
• Average 74.6
• Median 73

3
Midterm Question 3
4
Midterm Question 3

• Give the expressions of the input equations of
  each flip-flop.
• Give the expressions of the next states A and
  B, and the expression of the output Z.
• Draw the next state table.
• Draw the state diagram.
• Assume an input string of X111011. Give the
  corresponding output string Z after resetting the
  circuit.

5
Midterm Question 3
6
Midterm Question 3
7
State Encoding

• We have been using a binary state encoding
• S0 00
• S1 01
• S2 10
• S3 11
• There are other forms of state encoding
• One hot state encoding
• Gray code state encoding

8
One Hot State Encoding

• In one-hot state encoding, exactly one flip-flop
  stores a one in any state
• State one-hot binary
• S0 0001 00
• S1 0010 01
• S2 0100 10
• S3 1000 11
• More flip-flops, less next state logic
• More straightforward to implement
• State machine is just a shift register.

9
Gray State Encoding

• In grey scale state encoding, exactly one
  flip-flop changes to move from one state to
  another
• State Gray binary
• S0 00 00
• S1 01 01
• S2 11 10
• S3 10 11
• Timing is simpler Less chance of accidentally
  changing into wrong state

10
Traffic Light Controller

• Busy highway, small farm road controlled by a
  traffic light. The light is green in the highway
  direction unless a car comes on the farm road.
  The light cycles green in the farm direction for
  a short amount of time, then goes back to green
  in the highway direction.

11
Highway light timers

• TS Amount of time a light (in either direction)
  is yellow.
• TL Long timer. Minimum amount of time a light
  is green (in either direction). For farm light,
  amount of time light is green.
• The timer is a counter that counts all the time
• TS and TL are two outputs of this counter
• ST resets the counter to start counting again
  at 0

12
Controller Inputs and Outputs

• Inputs
• Reset
• TS Short timer
• TL Long timer
• Outputs
• HG, HY, HR Highway green, yellow, red
• FG, FY, FR Farm green, yellow, red
• ST Start Timer

13
State Diagram
14
State Table