The document describes the design of a 5-bit down counter digital circuit. It involves 6 steps: (1) drawing the state diagram, (2) constructing the next state table, (3) deriving the flip flop transition table, (4) mapping it on Karnaugh maps, (5) obtaining the logic expressions, and (6) drawing the final circuit diagram.

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UNIVERSITY OF KARACHI
5-Bit Down Prime Counter
Digital Electronics

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Step 1: State Diagram
11111
11101
10111
10011
10001
0110101011
00111
00101
00011
00010

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Step 2: Next State Table
Present State Next State
Q4 Q3 Q2 Q1 Q0 Q4 Q3 Q2 Q1 Q0
1 1 1 1 1 1 1 1 0 1
1 1 1 0 1 1 0 1 1 1
1 0 1 1 1 1 0 0 1 1
1 0 0 1 1 1 0 0 0 1
1 0 0 0 1 0 1 1 0 1
0 1 1 0 1 0 1 0 1 1
0 1 0 1 1 0 0 1 1 1
0 0 1 1 1 0 0 1 0 1
0 0 1 0 1 0 0 0 1 1
0 0 0 1 1 0 0 0 1 0
0 0 0 1 0 1 1 1 1 1
Step 3: Flip Flop Transition Table
Output Transition Flip Flop Input
QN QN+1 J K
0  0 0 X
0  1 1 X
1  0 X 1
1  1 X 0
QN : Present State
QN+1 : Next State
X Don’t Care

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Step 4: Karnaugh’s Map
J0
00 01 11 10 00 01 11 10
00 X X X 1 00 X X X X
01 X X X X 01 X X X X
11 X X X X 11 X X X X
10 X X X X 10 X X X X
= =
K0
00 01 11 10 00 01 11 10
00 X X 1 X 00 X 0 0 X
01 X 0 0 X 01 X X 0 X
11 X 0 X X 11 X 0 0 X
10 X X 0 X 10 X X X X
= =

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J1
00 01 11 10 00 01 11 10
00 X X X X 00 X 0 X X
01 X 1 X X 01 X X X X
11 X 1 X X 11 X 1 X X
10 X X X X 10 X X X X
= =
K1
00 01 11 10 00 01 11 10
00 X X 0 0 00 X X 1 X
01 X X 1 X 01 X X 0 X
11 X X X X 11 X X 1 X
10 X X 0 X 10 X X X X
= =

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J2
00 01 11 10 00 01 11 10
00 X X 0 1 00 X 1 0 X
01 X X X X 01 X X X X
11 X X X X 11 X X X X
10 X X 1 X 10 X X X X
= =
K2
00 01 11 10 00 01 11 10
00 X X X X 00 X X X X
01 X 1 0 X 01 X X 1 X
11 X 1 X X 11 X 0 0 X
10 X X X X 10 X X X X
= =

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J3
00 01 11 10 00 01 11 10
00 X X 0 1 00 X 1 0 X
01 X 0 0 X 01 X X 0 X
11 X X X X 11 X X X X
10 X X X X 10 X X X X
= =
K3
00 01 11 10 00 01 11 10
00 X X X X 00 X X X X
01 X X X X 01 X X X X
11 X 0 X X 11 X 1 0 X
10 X X 1 X 10 X X X X
= =

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J4
00 01 11 10 00 01 11 10
00 X X 0 1 00 X X X X
01 X 0 0 X 01 X X X X
11 X 0 X X 11 X X X X
10 X X 0 X 10 X X X X
= =
K4
00 01 11 10 00 01 11 10
00 X X X X 00 X 1 0 X
01 X X X X 01 X X 0 X
11 X X X X 11 X 0 0 X
10 X X X X 10 X X X X
= =

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Step 5: Logic Expressions for Flip-Flop Inputs
J0 = 1
K0 = Q4’ ∙ Q3’ ∙ Q2’
J1 = Q2
K1 = Q3 ∙ Q2 + Q4 ∙ Q2’+ Q4’ ∙ Q2
J2 = Q1’ + Q0’ + Q3
K2 = Q3’ ∙ Q4 + Q4 ∙ Q3’
J3 = Q0’ + Q1’∙ Q2’
K3 = Q2’ + Q1’ ∙ Q4
J4 = Q0’
K4 = Q1’ ∙ Q3’
Step 6: Circuit Diagram