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Computers
Question:
Today, the fastest PCs run at roughly 1.5 GHz.
Someday, computers may run at 1,000,000
GHz. Compared to present computers,
those high-speed ones would have to be
1. much larger.
2. much smaller.
3. about the same size.
Observations About Computers
• They respond to inputs with various outputs
• They handle all kinds of information
• Information is measured in bits and bytes
• Some information is lost when power fails
• Computers work extremely quickly
• They follow instructions perfectly
Analog Representation
• A number is represented by a physical quantity
– Current
– Voltage
– Magnetization
• Number is proportional to the physical quantity
• Precision is determined by the quantity itself
Digital Representation
• A numbers is represent by physical quantities
• Physical quantities take on discrete values
• These values represent pieces of the number
• Precision is determined by number of quantities
Binary Representation
• Each physical quantity has two values
– One value is defined as a “1”
– The other value is defined as a “0”
• Each quantity represents one information bit
• A number is represented by several bits
• The more bits, the more precision
• Bits are relatively immune to noise
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Example: 19
• Five bits can represent number from 0 to 31
• 19 is represented by the bits: 10011
• Each bit represents a power of 2
• 1·24 + 0·23 + 0·22 + 1·21 + 1·20 = 19
Representing Non-Numbers
• Bits or groups of bits are assigned to objects
– Characters
– Colors
– Days of the week
• 8 bits (a byte) can distinguish 256 objects
• Two bytes can distinguish 65,536 objects
Quantities Representing Bits
• Current
• Magnetization
• Charge
• Optical properties
• Light
• Radio Waves
• Sound
Computers & Bits
• Computation: currents
• Memory: charge
• Disk Drives: magnetization
• CDROM/DVDROM: optical properties
Computing
• Computers perform logical operations with bits
• Complicated operations based on simple ones
• Simplest operations: inversio