1. Faculty of Computers and Information
Cairo
University
Faculty of Computers and Information
Logic Design
CS221
1st Term
Counters

2. Administrivia homework #4 due next lecture
meeting with mentor TAs on wednesday
المشروعات الصغيرة: الخميس ٩ص-٥م
24/10/2009
cs221 – sherif khattab

3. serial adder
24/10/2009
cs221 – sherif khattab

4. serial adder with JK flip-flop
24/10/2009
cs221 – sherif khattab

5. serial adder with JK flip-flop
24/10/2009
cs221 – sherif khattab

6. universal shift register
24/10/2009
cs221 – sherif khattab

7. universal shift register
graphic symbol
24/10/2009
cs221 – sherif khattab

8. universal shift register
function table
24/10/2009
cs221 – sherif khattab

9. binary counters
an n-bit binary counter consists of n flip-flops and can count in binary from 0 through 2n - 1
Binary counters use flip-flops in complementing mode, such as:
T flip-flop with T=1
JK flip-flop with J=K=1
D flip-flop with D=Q'
24/10/2009
cs221 – sherif khattab

10. ripple counters A0 is complemented every clock cycle
A1: every time A0 goes from 1 to 0 (negative edge)
A2: every time A1 goes from 1 to 0 (negative edge)
24/10/2009
cs221 – sherif khattab

11. binary ripple counter
24/10/2009
cs221 – sherif khattab

12. synchronous counters All flip-flops have a common clock 24/10/2009
cs221 – sherif khattab

13. carry propagation when is C4 ready?
after 2 gates x 4 adders = 8 gate delays
24/10/2009
cs221 – sherif khattab

14. carry propagation
in order for second adder to have its inputs ready quickly, can we compute C1 from A0 and B0 and C0?
when is C1 = 1?
when A0 and B0 = 1 OR
(A0 NOT EQUAL B0 ) AND C0 = 1
Ci+1 = AiBi + (Ai XOR Bi) Ci
24/10/2009
cs221 – sherif khattab

15. carry propagation
24/10/2009
cs221 – sherif khattab