1. Binary Values
COSC 1323

2. Why Binary?
Electrical devices are most reliable when they are built with 2 states that are hard to confuse:
• gate open / gate closed
But we don’t physically open gates in electronic circuits. So:
Integrated circuit contains logic gates
Two inputs (on/1/closed or off/0/closed), a battery (E) and a lightbulb – if either or both gates are closed/on, the lightbulb comes on
4 possible combinations for input: 00, 01, 10, 11

3. Why Binary?
Electrical devices are most reliable when they are built with 2 states that are hard to confuse:
• gate open / gate closed
• full on / full off
• fully charged / fully discharged
• charged positively / charged negatively
• magnetized / nonmagnetized
• magnetized clockwise / magnetized ccw
These states are separated by a huge energy barrier.

4. Punch Cards hole No hole
hole
No hole

5. Jacquard Loom Invented in 1801
The point: binary was useful even before computers.

6. Jacquard Loom Invented in 1801
The point: binary was useful even before computers.
Picture on left from David Reed. A Balanced Introduction to Computer Science.

7. Everyday Binary Things
Examples:
Light bulb
Door locked
Refrigerator door closed
A/C on
Dishes dirty or clean
Garage door open
Alarm system set

8. Everyday Binary Things
Examples:
Light bulb on/off
Door locked/unlocked
Garage door up/down
Refrigerator door open/closed
A/C on/off
Dishes dirty/clean
Alarm set/unset
Light bulb
Door locked
Refrigerator door closed
A/C on
Dishes dirty or clean
Garage door open
Alarm system set

9. Binary (Boolean) Logic
If: customer’s account is at least five years old, and
customer has made no late payments
Then: Approve request for limit increase.
Point here: Boolean logic has two values: T and F

10. Number Systems
base: number of different digits which can occur in each position of a number
Decimal: base 10
digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Binary: base 2
digits 0, 1
Hexadecimal: base 16
digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
A for 10, B for 11, etc.

11. Exponential Notation 42 = 4 * 4 = 43 = 4 * 4 * 4 = 103 =
1011 = 100,000,000,000
Picked 10^11 because it’s about the number of neurons in human brain

12. Powers of Two
How many champions? How many teams in the championship? How many in the semi-finals? And so forth?

13. Powers of Two

14. Powers of Two 1 2 4 3 8 16 5 32 6 64 7
128
256 9
512 10
1024 11
2048 12
4096 13
8192 14
16384

15. Counting in Binary
0000
0001
0010
0011
0100
0101
...

16. My Android Phone
Ask students which category is bigger? Get them to sort of KB vs MB vs GB.

17. Naming the Quantities
10^15 = 1000^5.
103 = 1000
210 = 1024

18. Morse Code Uses dots and dashes
Similar concept to representing text with bits and bytes

19. Braille

20. Braille With six bits, how many symbols can be encoded?
2^6 = So Braille uses escape characters to indicate a larger alphabet.
Top to bottom on left (6 dots): 1,2, 3 On right: 4, 5, 6
Add 2 bits (7 and 8 on bottom): 8 raised – next letter is capitalized, both raised: next value is a number
With six bits, how many symbols can be encoded?

21. Binary Strings Can Get Really Long
Long, but why do we care?

22. Binary Strings Can Get Really Long
Long, but why do we care?
Colors consist of various amounts of red, green, blue
Color represented as RGB value, which is 3 numbers indicating the relative contribution of each of the three primary colors.
Each number in triple is on a scale from 0 to 255: 0 means none of that color, 255 means full contribution
(255, 255, 0): maximum contribution of red and green, no blue – bright yellow

23. Base 16 (Hexadecimal) 1111 1111 0011 1101 1001 0110 F F 3 D 9 6
Problem: binary strings are long and annoying to deal with for people
Flash to hex for colors also hex corresponds to four bits. So two hex symbols is one 8-bit byte.