1. Digital Circuit Why Digital Circuit? – Digital signals ( 0 and 1) are very easy to handle with electronic circuits only 2 states needed: Switch ON or OFF, Circuit CLOSED or OPEN, Current FLOWING or NOT, Voltage HIGH or LOW Low error: accurate measurement of voltage in analog circuit vs. 0 (0-2V) and 1 (2.6 to 5 V).

2. Why Digital Analog signal processing This is an “adder” circuit

3. Noise Problem Noise hampers our ability to distinguish between small differences in values  e.g. between 3.1V and 3.2V.

4. Value discretization Any numbers, letters, and symbols can be represented using multiple binary digits and coding, much like using multiple decimal digits to represent numbers greater than 9. E.G.: binary 101  5

5. Digital System

6. Better noise immunity Lots of “noise margin” –For “1”: noise margin 5V to 2.5V = 2.5V –For “0”: noise margin 0V to 2.5V = 2.5V Voltage thresholds and logic values:

7. What about 2.5V? Hmmm… create “no man’s land” or forbidden region For example

8. But, but, but… Where is the noise margin What if the sender sent 1: V H ? “1” noise margin: V IH -V OH “0” noise margin: V IL -V OL

9. Digital systems follow static discipline: if inputs to the digital system meet valid input thresholds, then the system guarantees its outputs will meet valid output thresholds

10. Review of Decimal Counting Most familiar! "Place holders" are powers of 10 Power of 10:3210 Weight:1000 100 10 1 10 3 10 2 10 1 10 0 Ten symbols or characters needed: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 1998 = (1 x 10 3 ) + (9 x 10 2 ) + (9 x 10) + 8 = 1000 + 900 + 90 + 8 Example

11. Binary Counting Base 10Base 2Base 10Base 2 0081000 1191001 201101010 311 1011 4100121100 5101131101 6110141110 7111151111 Digitizing a Signal

12. Binary Counting Power of 2:76543210 Decimal Weight:1286432168421 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 Example: convert 1100010 to decimal Binary Number:01100010 Decimal Weight of Placeholders: 128 64 32 16 8 4 2 1 Contributions to Decimal Number:0643200020 Answer: 64 + 32 + 2 = 98 "bit" is a contraction of "binary digit"

13. Conversion to binary 22=a n  2 n + a n-1  2 n-1 +…….+a 0 reminder 2110  a 0 =0 = a n  2 n-1 + a n-1  2 n-2 +..+a 1 2 51  a 1 =1 2 21  a 2 =1 2 10  a 3 =0 2 01  a 4 =1 22 = 10110

14. Addition of Binary number 1 + 0 = 1-- No surprise. 1 + 1 = 10-- Don't forget to carry! 1 + 1 + 1 = 11

15. Concept Check: Binary Counting In binary, which one of the following is not true? A: 10 + 10 = 110 B: 11 + 11 = 110 C: 101 + 1 = 110 Answer: A