Time-Division Multiplexing Realizations of Multiple-Output Functions Based on SMTMDD

1. Time-Division Multiplexing Realizations of
Multiple-Output Functions Based on
SMTMDD
Presented By:
Md. Ahasanul Alam

2. List of Contents
● Realization of Decision Diagram using Multiplexer
● Time Division Multiplexing (TDM)
● TDM realization of multi-output function
● Reducing required hardware in TDM realization
● Constructing Multiplexer using CMOS Logic
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3. How to Realize Decision Diagram?
x1 x2 f(x1,x2)
0 0 0
0 1 1
1 0 1
1 1 0
f(x1,x2) = x1 XOR x2
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4. Multiplexer (MUX)
Select
(S)
Output
(Y)
0 Ao
1 A1
● A Multiplexer is a device that allows one of several input signals which are to be
selected and transmits the input that is selected into a single medium.
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5. Multiplexer Based Circuit of BDD
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A
B C
A
B
C
0
0
1
1
Select
(X)
Out
(Y)
0 Ao
1 A1
Each Node is represented as a MUX

6. Multiplexer Based Circuit of BDD
1
For input = 01 (x1 = 0, x2 =
1)
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No. of MUX = 3

7. Time Division Multiplexing (TDM)
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● Time-division multiplexing is a method of transmitting and receiving multiple
signals over a common signal path by means of synchronized switches.

8. Multiple Output Functions
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SBDD

9. TDM Realization of Multi-Output Function based on SBDD
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10. Hardware Requirements in SBDD
● 19 2to1 MUX
● 6 Logic gates
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11. Shared Multivalue Decision Diagram (SMDD)
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x1 x2 X
(x1,x2)
f(x1,x2)
0 0 0 0
0 1 1 1
1 0 2 1
1 1 3 0
f(x1,x2) = x1 XOR x2

12. MUX Realizations Based on SMDD
● Use 4-valued input
● Use 4 to 1 MUX
● Requires less number of MUXs
X1 X2 f(x1,x2)
0 0 f0
0 1 f1
1 0 f2
1 1 f3 12

13. MUX Realizations Based on SMDD
13
2
3
0
1

14. Hardware Requirements in SMDD
● 11 4to1 MUX
● 6 Logic gates
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15. TDM Realizations Based on SMTMDD
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x1 x2 X
(x1,x2)
f1 f2 G
(f1,f2)
0 0 0 0 0 0
0 1 1 1 0 2
1 0 2 1 1 3
1 1 3 0 1 1
f1 = x1 XOR x2 & f2 = x1x2+x2

16. TDM Realizations Based on SMTMDD
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X
(x1,x2)
G
(f1,f2)
0 0
1 2
2 3
3 1
f1 = x1 XOR x2 & f2 = x1x2+x2

17. 4to1 MUX for SMTMDD
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18. Hardware Requirements in SMTMDD
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19. TDM Realizations Based on SMTMDD
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Y Y.ῆ f0 Y.η f1
0 0.ῆ 0 0.η 0
η η.ῆ 0 η.η 1
ῆ ῆ.ῆ 1 ῆ.η 0
1 1.ῆ 1 1.η 1

20. Hardware Requirements in SMTMDD
● 9 4to1 MUX
● 0 Logic gates
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21. Inside a Multiplexer
● Electronic devices are build with
○ Transistor
○ Intel core i-7 → 2.6 billion
○ Nvidia's H100 → 80 billion
● Basic Building block of transistor
○ Semiconductor
● Semiconductor used in MUX
○ Complementary Metal-Oxide Semiconductor (CMOS)
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22. Basic Concept of CMOS
● CMOS is the combination of
○ Positive Channel MOS (PMOS)
○ Negative Channel MOS (NMOS)
● PMOS
● NMOS
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s
s s
s
s
s

23. Basic Concept of CMOS
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s
s
Input output
0 1
1 0

24. 2to1 MUX using CMOS
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25. 2to1 MUX using CMOS
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For S=0

26. 2to1 MUX using CMOS
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For S=0

27. 2to1 MUX using CMOS
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For S=1

28. 2to1 MUX using CMOS
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For S=1

29. 4to1 MUX using CMOS
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30. Thank You
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