1. CS 111 – Aug. 27 Section 1.1 –Binary data and operations –Logic gates –Flip-flop –A binary shorthand: hexadecimal Commitment for next day: –Please read sections 1.2 and 1.3

2. Binary All information inside computer is in binary Smallest unit of data is the bit Only the values 0 and 1 are used 0 means “false” or “off” or the number 0 1 means “true” or “on” or the number 1 Individual bit values can be manipulated with Boolean operations: “and”, “or”, “not”, etc. –In hardware, we implement these operations with logic gates.

3. Boolean examples AND –To graduate, you must have 128 credits and 2.0 GPA. OR –Classics scholarship requires 3 years of Latin or 3 years of Greek. XOR (“exclusive” or) –To go to Cincinnati, you can fly or drive. In other words, it doesn’t make sense to do both. –Do you want a 2-door or a 4-door car? NOT –If a statement is true, its negation is false, and vice versa.

4. Gates Basic building blocks of CPU’s circuitry. Usually 2 inputs. X and Y could be 0 or 1. Combining gates into a circuit: –The output of one gate becomes input to another. –This is how more useful operations are performed.

5. ‘AND’ and ‘OR’ AND XYans 111 100 010 000 OR XYans 111 101 011 000 Note: 0 AND (anything) = 0 1 OR (anything) = 1

6. XOR XOR basically says, “either but not both” The output is 1 if both inputs are different. XOR XYAns 110 101 011 000

7. NOR, NAND NOR gate –Negation of the OR –Same as feeding output of OR into a NOT gate. –Symbol for NOR gate is same as OR but with a loop on the end. NAND gate –Negation of the AND…. analogous to NOR. Interesting property: –NOR and NAND are universal gates. Any other boolean operation can be implemented by using several NAND’s or several NOR’s.

8. Flip-flop circuit Circuit that can “store” or remember a 1 bit value. Its own output is used as input to one of its gates. To change flip-flop’s value, set one of the inputs to 1. See diagrams on page 23.

9. Hexadecimal One bit is not enough to convey much information. A single word or numerical value requires several bits. –Ex. The word “cat” can be represented by this bit sequence: 011000110110000101110011 “Hex” is a shorthand for binary –Allows us to represent every 4 bits with just 1 symbol. –Ex. 24 bits of information= 6 hex characters. –The word hexadecimal means there are 16 possible symbols, so we use 0-9 and then a-f. See table on page 25.