CS%20140L%20Lecture%205

1
CS 140L Lecture 5

• Professor CK Cheng
• CSE Dept.
• UC San Diego

2
Counters Synchronous counters Johnson
counters Odd Length counters
3
Synchronous Counter
Q
Q
Q
A
B
C
D
D
D
CLK
A B C A(t1) B(t1) C(t1) 0 0 0 0
0 0 1 1 0 0 1 0
1 0 2 0 1 0 0 1
1 3 0 1 1 1 0
0 4 1 0 0 1 0 1 5 1
0 1 1 1 0 6 1 1 0
1 1 1 7 1 1 1 0
0 0
C(t1) C(t) B(t1) B(t) C(t) A(t1)
A(t) (B(t)C(t))
4
Synchronous vs Asynchronous Counters

1. There are two things to keep track of cost vs.
   performance.
2. For example, the synchronous counter has better
   performance but higher costs due to the added
   gates. On the other hand, the asynchronous
   counter is easier to implement.
3. As the length of the counter increases, the cost
   increases, since the number of gates increases.

5
Johnson Counter A Shifter with An Inverted
Feedback Loop
A
B
C
Q
Q
Q
D
D
D
Q
CLR
CLK

1. Given n flip-flops, we have 2n states. Much less
   than previous counters. But Johnson is fast!
2. Only one output changes (low power).
3. Each output has n clock width (symmetrical).
4. Reset is needed. (ie, starts with 010, the
   counter ends up as 010-gt101-gt010-gt101)

Time Steps A B C

• 0 0 0
• 2 1 0 0
• 1 1 0
• 1 1 1
• 0 1 1
• 0 0 1
• 0 0 0

6
Odd Length Walking Ring CounterA Shifter with
Twisted Feedback Loops
A
B
C
Q
Q
J
J
Q
J
CLR
K
Q
K
Q
K
Q
Time Steps A B C

• 0 0 0 0
• 1 0 0
• 2 1 1 0
• 0 1 1
• 0 0 1
• 0 0 0
• 1 0 0
• 1 1 0

JA KA A (t1) 0 0 A(t) 0
1 0 1 0 1 1 1
A(t)
n JK F-Fs gt 2n-1 states The counter works itself
back to the proper sequence.
7
Pseudo Random Sequencer
Q
Q
Q
Q
D
D
D
D
CLK
n 4, length 15