1	Hardware
2	Where are we? Computer Science is the study of algorithms, including their Formal and mathematical properties We’re mostly done with this part Hardware realizations Computing Agents Linguistic realizations Applications
3	Computer Hardware Binary numbers are used to encode all forms of data, such as numbers and letters Electric circuits process and store binary data Simple gates can be combined to build circuits for any computation Boolean logic is a useful abstraction of electric circuits
4	Binary Representation of Information Detecting Voltage Levels Why not 10 levels? Would be unreliable Not enough difference between states On/Off Fully Charged - Fully Discharged Magnetized - Demagnetized
5	Binary Numbers Base 2 - digits 0 and 1 ___ ___ ___ ___ ___ ___ 2⁵ 2⁴ 2³ 2² 2¹ 2⁰
6	Converting Binary to Decimal The position of each digit determines its value for example, the binary number 101011 equals: 1x2⁵ + 0x2⁴ + 1x2³ + 0x2²+ 1x2¹ + 1x2⁰= 32 + 0 + 8 + 0 + 2 + 1 = 43₁₀ note the similarity with decimal numbers: 572₁₀= 5x10² + 7x10¹ + 2x10⁰
7	Calculating in binary First practice counting to 20₁₀ in binary Practice adding: 1011₂ + 101₂ Try subtracting: 1011₂ - 101₂
8	Shorthand Notation Octal (Base 8) digits 0-7 Hexadecimal (Base 16) digits 0-F ___ ___ ___ ___ ___ ___ 8⁵ 8⁴ 8³ 8² 8¹ 8⁰ ___ ___ ___ ___ ___ ___ 16⁵ 16⁴ 16³ 16² 16¹ 16⁰
9	Binary numbers can represent all types of data negative integers: reserve the leading bit for sign (0=positive; 1=negative) letters: ASCII codes (using 8 bits=1 byte) A = 01000001, B=01000010, C=01000011, and so on… Why do they call it a byte? What is 4 bits called? Other digital data: MP3, DVD, JPEG, etc.
10	A Switch is a 2-state device that can be toggled A relay is a switch built with an electromagnet
11	Switches can do it all With switches we can implement AND, OR, and NOT gates With just those types of gates, we can design circuits to perform any computation
12	Basic electric circuits: Computing AND
13	Basic electric circuits: Computing OR
14	Basic electric circuits: Computing NOT
15	A better switch: Transistors bi-stable, solid state device switching is done electronically, not mechanically no moving parts; therefore, fast, small, reliable can switch states in about one 10 billionth of a second about 5 million transistors can fit on a chip 1 centimeter square. Density is increasing rapidly with new technology.
16	Summary Computers use binary numbers for storage and computation because all types of data can be stored this way 2-state devices are highly reliable A switch is a 2-state device that can be toggled Switches can implement AND, OR, and NOT gates With these gates, we can perform any computation, as we’ll see next time!