CSE115: Introduction to Computer Science I Dr. Carl Alphonce 219 Bell Hall 1

Announcements Recitations begin next week for TWF groups. Th recitations begin the week after. Put your name sign out! Cell phones off. 2

Today Representing things –information encoding –symbol interpretation A computer is a very simple machine –it manipulates voltages –gates are used to control voltage flow –circuits are combinations of gates –a flip-flop is a circuit that remembers But first… 3

Name sign competition And the winners are: 9:00 AM – KAYLA 3:00 PM – STEPHANIE 4

Counting Decimal (base 10) etc. Binary (base 2) etc. 5

Number systems Decimal (base 10) Each position is weighted by a power of 10. E.g. 734 = –7* *10 + 4*1 –7* * *10 0 E.g = –1* * *10 + 1*1 –1* * * *10 0 Binary (base 2) Each position is weighted by a power of 2. E.g. 111 = –1*4 + 1*2 + 1*1 = “seven” –1* * *2 0 E.g = –1*8 + 1*4 + 0*2 + 1*1 = “thirteen” –1* * * *2 0 6

Same information Different encoding Color (RGB & CMYK) Quantity (Decimal & Binary) 7

Bit string A ‘0’ or ‘1’ is a binary digit, or a bit. A sequence of bits is called a bit string. For example: –1101 is a bit string 8

Interpretation QUESTION: –What does the bit string 1101 represent? 9

Interpretation QUESTION: –What does the bit string 1101 represent? ANSWER: –Whatever we want it to represent! 10

Bit-string representations (used in computers) Binary (non-negative numbers) Two’s complement (integers) IEEE 754 (approx. floating point numbers) ASCII / EBCDIC / Unicode (characters) etc. 11

Questions? 12

physical vs. logical perspectives Physical reality: Logical view: WIRE Carries a HIGH voltage or a LOW voltage WIRE Carries a 1 or a 0 13

Idea 14

Controlling flow 0 15

Controlling flow 1 16

Two in a row? 0 17

Two in a row? 0 18

Two in a row? 0 19

Two in a row? 1 20

AND gate For which input values is output 1? For which input values is output 0? inputs are on left output is on right 21 0 or 1

Truth table for AND Input 1Input 2Output

OR gate For which input values is output 1? For which input values is output 0? inputs are on left output is on right 23

Truth table for OR Input 1Input 2Output

NOT gate For which input value is output 1? For which input value is output 0? input is on left output is on right 25

Truth table for NOT InputOutput

Flip-flop (a bit of memory!) S (set) R (reset) remembered value 27

Setting the flip-flop The normal value of R and S is zero. S (set) = 0 R (reset) = 0 remembered value 28

Setting the flip-flop To store 1 in the flip-flop, we “raise” S to 1… S (set) = 1 R (reset) = 0 remembered value 29

Setting the flip-flop …which makes the output of the OR gate 1. S (set) = 1 R (reset) = 0 remembered value 30 1

Setting the flip-flop The NOT gate inverts this 1 value to 0, which becomes the second input to the upper OR gate. S (set) = 1 R (reset) = 0 remembered value

Setting the flip-flop Since both inputs of the upper OR gate are zero, its output is zero. S (set) = 1 R (reset) = 0 remembered value

Setting the flip-flop The NOT gate inverts this 0 to a 1; this value becomes the second input to the bottom OR. S (set) = 1 R (reset) = 0 remembered value

Setting the flip-flop Because the output of the bottom OR gate will now stay at 1, we can lower S to zero, and the circuit will stay in a stable state, with 1 as the remembered value! 34 Resetting the flip-flop Resetting the remembered value to zero is similar, except we raise, then lower, the value on R. S (set) = 0 R (reset) = 0 remembered value

Recap Bit string by itself does not carry meaning. Bit string can be interpreted under a given representation scheme, which allows us to recover the encoded meaning. Circuits made from simple gates let us store and manipulate bit strings. 35

Questions? 36