This document describes the design of a synchronous binary irregular counter with a counting sequence of 0011, 1100, 0000, 1000, 0100. It includes a state diagram, next-state table, Karnaugh maps to simplify the logic expressions, and a logic diagram for implementation. Specifically, it covers an introduction to counters, defines a synchronous counter, shows the state diagram and next-state table, uses K-maps to minimize the logic expressions for J0-J3 and K0-K3, and provides the final logic expressions and diagram for implementation.

1. DESIGNING A
SYNCHRONOUS
BINARY IRREGULAR
COUNTER
WITH COUNTING
SEQUENCE

2. Prepared By
Name: Rokon, Md. Shafaat Jamil
ID: 17-33084-1

3. Topics To Be Covered
 Introduction
 State Diagram
 Next-State Table
 K-Map
 Counter Implementation

4. Introduction
 Counter
• A counter is a device which can count any particular
event on the basis of how many times the particular
event(s) is occurred .
 Synchronous Counter
 Synchronous Counters are so called because the clock
input of all the individual flip-flops within the counter are
all clocked together at the same time by the same clock
signal

5. State Diagram
0011
(3)
1100
(12)
0000
(0)
1000
(8)
0100
(4)

6. Flip Flop Transition Table
.

7. Next-State Table
Q3 Q2 Q1 Q0 Q3 Q2 Q1 Q0 J0 K0 J1 K1 J2 K2 J3 K3
0 0 1 1 1 1 0 0 X 1 X 1 1 X 1 X
1 1 0 0 0 0 0 0 0 X 0 X 0 1 X 1
0 0 0 0 0 1 0 0 0 X 0 X 1 X 1 X
0 1 0 0 0 1 0 0 0 X 0 X 1 X X 1
Present
State
Next State
0 1 0 0 0 0 1 1 1 X 1 X X 1 0 X

8. K-Map
0 X X X
1 X X X
0 X X X
0 X X X
00
01
11
10
00 01 11 10Q3Q2
Q1Q0
X X 1 X
X X X X
X X X X
X X X X
00
01
11
10
00 01 11 10Q3Q2
Q1Q0
J0 Map K0 Map

9. K-Map Cont...
.
0 X X X
1 X X X
0 X X X
0 X X X
00
01
11
10
00 01 11 10
Q1Q0
X X 1 X
X X X X
X X X X
X X X X
00
01
11
10
00 01 11 10Q3Q2
Q1Q0
J1 Map K1 Map

10. K-Map Cont...
.
0 X 1 X
X X X X
X X X X
1 X X X
00
01
11
10
00 01 11 10
Q1Q0
X X 1 X
X X X X
X X X X
X X X X
00
01
11
10
00 01 11 10Q3Q2
Q1Q0
J2 Map K2 Map
Q3Q2

11. K-Map Cont...
.
1 X 1 X
0 X X X
X X X X
1 X X X
00
01
11
10
00 01 11 10
Q1Q0
X X X X
X X X X
1 X X X
1 X X X
00
01
11
10
00 01 11 10Q3Q2
Q1Q0
Q3Q2
J3 Map K3 Map

12. Logic Expressions
J0 = Q2Q3’
K0 = 1
J1 = Q2Q3’
K1 = 1
J2 = Q0+Q3
K2 = 1
J3 = Q2’
K0 = 1

13. Counter Implementation
(Drawing)
.