1 EG 32 Digital Electronics Thought for the day You learn from your mistakes..... So make as many as you can and you will eventually know everything.

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Presentation transcript:

1 EG 32 Digital Electronics Thought for the day You learn from your mistakes..... So make as many as you can and you will eventually know everything

2 Digital Electronics Analog signal:Signal is constantly changing levels Digital signal:Signal is either present (1) or not (0) Computers Communications Music

3 Why Digital?

4 Noise:Clarity of signal Storage:Real time storage Programmable:Processing is easier Precision:Not dependent on component values Circuit Density:Much higher than analog

5 Basic Binary Arithmetic Decimal system-Base 10 Binary system-Base 2 Octal system-Base 8 Hexadecimal System-Base 16 Decimal system: = 2x x x x x x x10 -3 Binary system: = 1x x x x x x x2 -3 = = Each of the binary numbers is called a “bit”

6 Adding binary numbers x x x x 2 0 = 10 0 x x x x 2 0 = 7 16

7 Representation of Binary Signals

8 All Logic Circuits can be realized with just three basic building blocks Inverter And Gate Or Gate

9 Truth Table A table that lists all possible outputs for all possible inputs A BC n possible combinations AND Gate C = A  B “AB” Boolean expression:

10 Operation of AND Gate

11 A BC OR Gate Boolean expression: C = A + B

12 AC Inverter (“Not”) Boolean expression: C = A

13 NAND Gate A BC Boolean expression: C = A  B C = AB

14 NOR Gate A BC Boolean expression: C = A + B

15 A B A  B C X = A  B + C

16 To go the other way: Suppose we want to implement: Need a three-input OR Gate

17 Need two two-input AND Gates Need one three-input AND Gate Need two inverters

18 Exclusive OR (XOR) Gate A BC XOR Gate Boolean expression: C = A + B

19 The XOR gate can be used to make a circuit that adds two one - bit binary numbers = 0 no carry = 1 no carry = 0 1 carry

20 Adding binary numbers x x x x 2 0 = 10 0 x x x x 2 0 = 7

21 Boolean Algebra Theorems x  0 = 0 x  1 = x x  x = x x  x = 0 x + 0 = x x + 1 = 1 x + x = x x + x = 1 Single variable x + y = y + x x  y = y  x x + (y + z) = (x + y) + z = x + y + z x (yz) = (xy)z = xyz x(y + z) = xy + xz (w + x)(y + z) = wy + xy + wz + xz x + xy = x x + xy = x + y Multiple variables

22 Example: Simplify Factor out

23 DeMorgan’s Theorems (x + y) = x  y (x  y) = x + y Example: Simplify z = (A + C) + (B + D) z = (A  C) + (B  D) A = A, D = D z = AC + BD

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