ITECH1100 Understanding the Digital Revolution

ITECH1100 Understanding the Digital Revolution

Task 1 – Truth tables and logic circuit diagrams

Task 1A 

ABCXY
00000
00101
01000
01101
10000
10101
11011
11111

ABCXY
00000
00111
01011
01100
10001
10110
11010
11101

Task 1B

Task 1C

ABC
Do I see a clownAm I at circusRun away
000
010
101
110

ABCD
HungryLunchtimeHave foodShould I eat
0000
0010
0100
0110
1000
1010
1100
1111

ABCXY
Main switchLamp 1Lamp 2A.BA.C
00000
00100
01000
01100
10000
10101
11010
11111

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

282726252423222120
2561286432168421

  • 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

ABCXY
FALSEFALSEFALSEFALSEFALSE
FALSEFALSETRUEFALSETRUE
FALSETRUEFALSEFALSEFALSE
FALSETRUETRUEFALSETRUE
TRUEFALSEFALSEFALSEFALSE
TRUEFALSETRUEFALSETRUE
TRUETRUEFALSETRUETRUE
TRUETRUETRUETRUETRUE

(Refer – logic_diagrams.xlsx)

Task 3 B

ABCXY
FALSEFALSEFALSEFALSEFALSE
FALSEFALSETRUETRUETRUE
FALSETRUEFALSETRUETRUE
FALSETRUETRUEFALSEFALSE
TRUEFALSEFALSETRUEFALSE
TRUEFALSETRUEFALSETRUE
TRUETRUEFALSEFALSETRUE
TRUETRUETRUETRUEFALSE

(Refer – logic_diagrams.xlsx)

Task 4 – Full Adder

Task 4 A

INPUTOUTPUT
ABCSUMCARRY
00000
00110
01010
01101
10010
10101
11001
11111

Task 4B

A1B1S1C1
0000
0110
1010
1101

A2B2C1S2C2
00000
01010
10010
11111

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.