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Understanding the Digital Revolution

Task 1 – Truth tables and logic circuit diagrams

Task 1A 

A B C X Y
0 0 0 0 0
0 0 1 0 1
0 1 0 0 0
0 1 1 0 1
1 0 0 0 0
1 0 1 0 1
1 1 0 1 1
1 1 1 1 1

A B C X Y
0 0 0 0 0
0 0 1 1 1
0 1 0 1 1
0 1 1 0 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 0 1

Task 1B

Task 1C

A B C
Do I see a clown Am I at circus Run away
0 0 0
0 1 0
1 0 1
1 1 0

A B C D
Hungry Lunchtime Have food Should I eat
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1

A B C X Y
Main switch Lamp 1 Lamp 2 A.B A.C
0 0 0 0 0
0 0 1 0 0
0 1 0 0 0
0 1 1 0 0
1 0 0 0 0
1 0 1 0 1
1 1 0 1 0
1 1 1 1 1

Task 2 – Binary and representing integers

Task 2A

  • 2 bits

1 bit = 2 values

2 bits = 4 values

  • 1 byte

1 byte = 8 bits

=28

= 256 values

  • 6 byte

6 byte = 48 bits

= 248

= 2.81 X 10 14

  • 128 bits = 2128

= 43.40 X 1038

Task 2B

  • 3
  • 7
  • 8
  • 12
  • 77

Task 2C

28 27 26 25 24 23 22 21 20
256 128 64 32 16 8 4 2 1
  • 10

= 1 X 21 + 0 X 20

= 2 + 0

= 2

  • 111

= 1 X 21 + 1 X 21 + 1 X 20

= 4 + 2+ 1

= 7

  • 1101

= 1 X 23 + 1 X 22 + 0 X 21+ 0 X 21+ 1 X 20

= 16 + 0 + 4 + 2 + 0

= 22

  • 10110

= 1 X 24 + 0 X 23 + 1 X 22 + 1 X 21+ 0 X 20

= 16 + 0 + 4 + 2 + 0

= 22

  • 100110

= 1 X 25 + 0 X 24 + 0 X 23 + 1 X 22 + 1 X 21+ 0 X 20

= 32 + 0 + 0 + 4 + 2 + 0

= 38

  • 1000100

= 1 X 26 + 0 X 25 + 0 X 24 + 0 X 23 + 1 X 22 + 0 X 21+ 0 X 20

= 64 + 0 + 0 + 0 + 4

= 68

Task 3 – Excel as a logic calculator

Task 3A

A B C X Y
FALSE FALSE FALSE FALSE FALSE
FALSE FALSE TRUE FALSE TRUE
FALSE TRUE FALSE FALSE FALSE
FALSE TRUE TRUE FALSE TRUE
TRUE FALSE FALSE FALSE FALSE
TRUE FALSE TRUE FALSE TRUE
TRUE TRUE FALSE TRUE TRUE
TRUE TRUE TRUE TRUE TRUE

(Refer – logic_diagrams.xlsx)

Task 3 B

A B C X Y
FALSE FALSE FALSE FALSE FALSE
FALSE FALSE TRUE TRUE TRUE
FALSE TRUE FALSE TRUE TRUE
FALSE TRUE TRUE FALSE FALSE
TRUE FALSE FALSE TRUE FALSE
TRUE FALSE TRUE FALSE TRUE
TRUE TRUE FALSE FALSE TRUE
TRUE TRUE TRUE TRUE FALSE

(Refer – logic_diagrams.xlsx)

Task 4 – Full Adder

Task 4 A

INPUT OUTPUT
A B C SUM CARRY
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1

Task 4B

A1 B1 S1 C1
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
A2 B2 C1 S2 C2
0 0 0 0 0
0 1 0 1 0
1 0 0 1 0
1 1 1 1 1

References

  • Aberg, R. O., Raghavan, V., & Ren, Y. (2014). U.S. Patent No. 8,798,971. Washington, DC: U.S. Patent and Trademark Office.
  • Gale, E., de Lacy Costello, B., & Adamatzky, A. (2013, July). Boolean logic gates from a single memristor via low-level sequential logic. In International Conference on Unconventional Computing and Natural Computation (pp. 79-89). Springer, Berlin, Heidelberg.
  • Smessaert, H., & Demey, L. (2016, August). Visualising the Boolean Algebra $$\mathbb {B} _ {4} $$ in 3D. In International Conference on Theory and Application of Diagrams (pp. 289-292). Springer, Cham. 
  • Whitesitt, J. E. (2012). Boolean algebra and its applications. Courier Corporation.
  • Wilkins, C. (2012). Digital electronics and laboratory computer experiments. Springer Science & Business Media.