How Computers Work
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How Computers Work, Lecture Notes - Computer Science, Study notes of Introduction to Computers
Bits, Building Block, Logic Gates, AND OR XOR Gates, Base-2 Addition, Column Adder, Level of Abstraction
Typology: Study notes
2010/2011
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How Computers Work
Review
When we compute, we operate on discrete / digital values. Examples of digital machines:
The Most Important Part
What is the most important part of your computer? Your computer's processor (CPU) What companies manufacture CPUs? Intel, AMD, etc. The processor is the computer's brain. It's what runs your programs.
Today's Plan
Lofty Goal: Learn how processors work. But: Your processor is a complex digital machine. So: Learn how simple digital machines work. Hope: Give you a sense for how some of the things inside your processor work. (This is what ECE majors study.)
How many possible values ...
... can I represent with 2 bits? 4: 00, 01, 10, 11 ... can I represent with 3 bits? 8: 000, 001, 010, 011, 100, 101, 110, 111 ... can I represent with n bits? 2 n
How many bits do I need ...
... to represent 3 possible values? 2 ... to represent 6 possible values? 3 ... to represent 20 possible values? 5
Bits and Voltage
Lower voltage = "0" Higher voltage = "1" Each wire carries a single bit. We can literally determine whether a wire is carrying a "0" or a "1" by measuring the voltage on that wire.
Our Building Blocks
A NOT Machine Its Truth Table 1 0 0 IN OUT 1 NOT IN OUT 0 = false 1 = true
Our Building Blocks
An OR Machine Its Truth Table 0 1 1 1 0 B OUT 1 0 A 0 0 1 1 1 B A OUT OR
Logic Gates
These 3 machines are referred to as logic gates. An AND machine (for example) is referred to as an AND gate.
A Detour: Happy Robots
The robot is happy if leftHasWall() or rightHasWall() , but not both. lonely claustrophobic happy happy
Write isHappy without an if
public static boolean isHappy() { return _______________________ _______________________; } (leftHasWall() &&! rightHasWall()) || (! leftHasWall() && rightHasWall())
Building An XOR Machine
(A AND (NOT B)) OR ((NOT A) AND B)
AND OUT OR NOT NOT AND A B
Remember: Abstraction
Once we defined turnRight to mean Robot.turnLeft(); Robot.turnLeft(); Robot.turnLeft(); we could now think of turnRight as one of our building blocks. This idea is called Abstraction.