# Task 1 – Truth tables and logic circuit diagrams

 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

 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

• 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

• 3
• 7
• 8
• 12
• 77

 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

 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)

 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)

 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

 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.