1. The First lesson on Digital Logic Rachaen M. Huq1 Rachaen Huq. Dept. of EEE, BRACU

2. Binary LOGIC, Boolean variables Rachaen M. Huq2 “A”, “B”, and “Lamp” are Binary Variables, i.e. can take values only 1 and 0 (only two states) See the table for ALL Possible combinations of A, B, and Lamp A practical example ABLamp 000 010 100 111 Its called a Binary AND Logic

3. Representation of AND Rachaen M. Huq3 Note the symbol of an AND Logic, a.k.a. AND Gate. There are other symbols for other kind of logics. Its called a GATE because the inputs are given to the “gates” of the MOSFETS. Hence, the logic gate symbols exist in reality as a combination of MOSFETS. The inputs are either a Low, (0V or -5V) or High(5V). Low =0, High = 1. Expressed as: Output = A.B The expression is a Boolean algebraic equation, driven by Boolean variables “output”, “B” and “B”. This logical relationship table is called a truth table

4. Inside an AND GATE Rachaen M. Huq4 Apply 5V in Both A and B, you will get 5V in “Out” directly from Vdd biasing (5V). Any of them is 0V, the line disconnects, but below, one line is activated which makes OUT to be connected to Vss- (0V).

5. Practical Example of an OR Gate Rachaen M. Huq5 Expressed as: Output = A + B

6. NOT gate (inverter) Rachaen M. Huq6 Note that a NOT gate can have only ONE input and only ONE output Expressed as: C = A’

7. Summary of Basic gates Rachaen M. Huq7 AND/OR Gates may have more than two inputs… Depending one How many MOSFETS are in series/parallel! Guess the truth tables

8. Other gates Rachaen M. Huq8 Output = ??

9. Rachaen M. Huq9 NAND Negative OR Invert First Then OR ABCOut = C’ ABAB Out ABAB AA’BB’Out C

10. Do the same for NOR and Neg. AND You will find that they eventually lead to Boolean algebraic identities. (A+B)’ = A’. B’ (AB)’ = A’ + B’ Its called De Morgan’s Law. This is just an identity which applies in Boolean Algebra, just like the (a+b)^2 identity applies in traditional algebra. Rachaen M. Huq10

11. Exclusive (X-__) gates Rachaen M. Huq11 Symbol? Output = A__?__B Symbol? Output = A__?__B

12. A summary of all the gates are available at Section 2-7 Morris Mano Page 57 Rachaen M. Huq12

13. Boolean Equations A Boolean variable (which can have the values of 0 or 1 only), represented as a result of (multiple) Boolean operations. Boolean variables: a,b,c,x,y,z, just like any variable. Booleans operations: AND, OR, NOT Examples: Rachaen M. Huq13

14. Connected logic gates, more complex functions See blackboard for examples. Rachaen M. Huq14