BA 370 - Hardware & Binary Systems

 

• Our hardware is a system: elements, relations, inputs, outputs, etc.
• Stair & Reynolds: three types of elements:
1. Input devices: import data from the system's environment.
2. Processing devices: process inputs and generate outputs:
• Central Processing Unit (CPU): orchestrates arithmetic and logical operations and can be modeled as a subsystem:
• Arithmetic Logic Unit (ALU): performs all arithmetic and logical operations.
• Control unit: orchestrates the ALU.
• Memory (registers, cache, etc.).

• Memory (Stair & Reynolds, p. 98):

• Permanent: disks (hard, floppy, CD etc.), tapes, sticks, chips, etc.)
• Nonvolatile: Read Only Memory (PROM, EPROM, EEPROM, etc).
• Volatile: 
• CPU-resident memory.
• Other 'processor-resident' memory; e.g., video card memory.
  
• Random Access Memory (RAM: various types).
• Virtual Memory, RAM disk, swap space, etc.
  

• Bus.
  
• Video card.
• Network Interface Card.
• Etc.
  

3. Output devices: export data to the system's environment: e.g.,screen, printer, speakers, etc.

   Problem: Is a disk drive an output device or a processing device?

• Performance:
• Clock speed: Hz, KHz, MHz, GHz, THz, etc. (Heinrich R. Hertz (1857 - 1894); experimentally confirmed the existence of electromagnetic waves).
• Instructions per Second: MIPS, BIPS.
• FLoating Point Operations per Second: MFLOPS, GFLOPS, TFLOPS.
• However, must factor in:
• CPU architecture; e.g. RISC (p. 97).
  
• Number of bits used per activity: bus line width & CPU wordlength  (16-bit, 32-bit, 64-bit, etc.):
• First, a word on bits and bytes:
• Computers are logical machines --> all data consist of true/false, on/off combinations.
• A simple switch (or bit) has two states: on/off (true/false).
• An array of eight such switches (byte) has 2⁸ = 256 possible states.
• In (digital) computers, all data are represented this way.
• For instance, numbers can be expressed this way --> binary number or base-2 representation:
• Let: a bit can be on (1) or off (0).
• Let: a bit represent a power of 2.
• Let: the right most bit represent the lowest power (0):
• 111₂ = 2⁰ (1) + 2¹ (2) + 2² (4) = 7₁₀. 
• 101₂ = 2⁰ (1) +  2² (4) = 5₁₀. 
• 100₂ = 2² (4) = 4₁₀. 
• Note that in this binary system, we have only two symbols: 0 and 1.
• In our decimal (base 10) system we have ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• In both systems the same counting rules hold:
• 111₁₀ = 10⁰ (1) + 10¹ (10) + 10² (100) = 111₁₀. 
• 101₁₀ = 10⁰ (1) +  10² (100) = 101₁₀. 
• 173₁₀ = 3 * 10⁰ (3) + 7 * 10¹ (70) + 1 * 10² (100) = 173₁₀. 

• Arithmetic works identically in both systems:
• Binary: 11 (3) + 10 (2) = 101 (5) (use 'carry').
• Decimal: 97 + 10 = 107 (use 'carry').

• Remember that a in C or VB.NET a short is a (two-byte) integer: -32768 <= short <= 32767.
• 32767 = 2¹⁵ - 1
• two bytes = 16 bits.
• 1 bit required for sign ==> 15 bits available for value ==> 32768 combinations.
• One combination (all bits off) reserved for zero.
• Left: 2¹⁵ - 1.

• Problem: Why is the smallest number -32768 rather than -32767?
• What about zero?  Are 0 and -0 both zero? (nasty).
• Two's complement: Invert the (positive) binary number and add 1.
• Note: all two's complement numbers starting with (most significant bit) a 1 are negative.
• -13₁₀ ==> 01101 ==> 10010 ==> + 1 = 10011₂.
• -0₁₀ ==> 0000 ==> 1111 ==> + 1 = (1)0000 = 0000₂ (odometer).

• 
  
  TC:     0000          0111  1000                   1111
  
  ---------|--------------|-----|----------------------|
  
  Decimal: 0              7    -8                     -1
  
  

• Hence, smallest short under two's complement = -37,768!!
• Arithmetic rules hold just fine:
• 7₁₀ + -2₁₀ = 
• 0000 0111 + (0000 0010 => 1111 1101 ==> + 1 =) 1111 1110) = 
• (1)00000101 = +5₁₀
 
• Floating point numbers; e.g., 1.99 or 123.56789 can be represented likewise, but in multiple parts.
• Other counting systems; e.g., hexadecimal or 'hex' counting: 16 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
• 10₁₀ ==> A₁₆
• Font color in HTML: RxGxB = 256³ = 16,777,216 colors (24(32)-bit color depth)
• White in RGB: 255, 255, 255
• White in hex: FFFFFF

• Need fewer symbols for larger numbers.

• Problem: What about 'irrational' numbers such as pi?
  

• Characters (e.g., ASCII and Unicode).

• Memory addressing:
• 16 bit --> 2¹⁶ --> 65,536 Bytes = 64KB (1 KB = 1,024 Bytes).
• 32 bit --> 2³² --> 4.29e09 = 4,294,967,296 = 4,194,304 KB = 4,096 MB.
• 64-bit --> 2⁶⁴ --> 1.84e19 = ... rather a lot.

• Precision of numbers, speed of floating point computation.
• Throughput: data traffic 'chunk' size.
  

• Amount and speed of (virtual) memory.
• Bus speed.
  
• Operating System.
• Examples:
• Sun Blade 150 Workstation (no display!):
• 550 MHz.
• 64-bit computing.
• UltraSparc (RISC)
• 256M RAM.
• 80 GB HD.
  
• Sun Solaris.
• $1,395.
  
• Dell Dimension 3000:
• 2.8 GHz.
• 32-bit computing.
• Intel Pentium 4.
• 256M RAM.
• 80 GB HD.
  
• Microsoft XP Professional.
• $599.

• Apple Power Mac G5 (no display!!):
• 2.0 GHz.
• 64-bit computing.
• POWERPC G5  (second generation RISC)
• 512M RAM.
• 160 GB HD.
  
• MAC OS X.
• $2,000.