CS 40 - Lecture 10

Cay S. Horstmann

How Computers Work

• Everything is a number (in binary)
• Small number of very primitive instructions (move, add, jump) ...
• ...executed very quickly
• That's all
• Computers aren't smart

Everything is a Number

• Letter A = 65, B = 66, C = 67, ... , d = 100, ...
• = 38651
• Unicode defines about 100,000 characters (about 80% used for Chinese/Japanese/Korean)

Everything is a Number

• pixel position = x, y values
• line = collection of pixels
• 
  (1,1) (2,1) (3,2) (4,2) (5,3) (6,3) (7,3) (8,4) (9,4) (10,5) (11,5)

Everything is a Number

• Color = 3 numbers (red, green, blue)
  
• Pink = 255 192 203

Binary Numbers

• Easier to build electric circuits with on/off than with 10 levels of voltage
• Any number can be expressed in binary
• Instead of ones, tens, hundreds, thousands, etc, use
  1, 2, 4, 8, 16, 32 (powers of two)
• Example: 101110 = 1·32 + 0·16 +1·8 +1·4 + 1·2 + 0·1 = 46

Lab: Binary Numbers

Lab: Binary Numbers

• Load Binary.a2w into Alice (link in schedule)
• What is 111000 in decimal? Ask Cleopatra.
• Through trial and error, find the binary value for 44.
• Answers in ActiveLecture.org

Computer Architecture

Computer Architecture Terms

• CPU = central processing unit. Fetches program instructions, transfers data, does arithmetic computations
• RAM = random access memory. Stores numbers. (Everything is a number.)
• These are silicon chips. They stop working/storing when the power is off.
• Hard disk also stores numbers, using tiny magnets. Storage needs no power, but retrieval does.

Simplified Architecture

Architecture Details

• CPU has registers. Each register holds a single number.
• Modern CPU have 10 or more registers. Our simple computer has one, called AX
• Each memory location holds a single number.
• Each memory location has an address (also a number): 0, 1, 2, 3, ...
• Modern computer memory holds a few billion numbers. Our simple computer holds 100 (addresses 0 - 99).
• The program counter (PC) contains the address of the next instruction

Architecture Details

Instructions

• Each computer has a set of instructions. Modern computer has hundreds. Our simple computer has 13.
• Typical instructions:
  • Move contents of memory location i to register
  • Move register contents to memory location i
  • Add contents of memory location i to register
  • Jump to instruction at memory location i
• For human convenience, instructions have mnemonics. Ex. ADC = add with carry

Everything is a Number

• Instructions are numbers
  

• In our simple computer, LOAD=161, SUBI = 45, JPOS = 127, HALT = 0
• See http://community.vcsu.edu/facultypages/curt.hill/My_Webpage/computer.html

BE the Computer

• Simple computer program (starts at memory location 0)
  161 7 45 1 127 2 0 3

BE the Computer

Lab 2: BE the Computer

Lab 2: BE the Computer

• ON PAPER, simulate this program.
• What values are in cells 97, 98, 99 when the program halts? ActiveLecture.org
• What does the program do? (I.e if you put a different number into cell 99 and ran it, what would it compute in general?) ActiveLecture.org

Lab 2: Run the Simulator

• Now run the simple computer simulator (link on schedule)
• Type in the same program
• What does the Single Step button do?
• What result do you get? ActiveLecture.org

Too Boring?

• Write a program that computes powers of two
• Cell 49 contains the number of powers that you should compute
• Put 1 2 4 8 ... into cells 50, 51, 52, 53...,
• If cell 49 contains 10, then you compute up to 2¹⁰ in cell 59
• Run the simulator.
• Congratulations! You are an assembly programmer!

Food for Thought

• If computers are so dumb, how can they decide whether I get a loan?
• How can you decide anything with just adding, moving, and jumping?
• What else do our brains do?