Some Things from 125

• Numbers
  • How do you convert the number 4315 to binary?
  • How do you convert 10111010₂ to decimal?
  • How many positive integers can you represent with 4 bits? With n bits.
  • What is the range of integers that can be represented with n bits.
  • What is hexadecimal (hex)?
  • Why do we use hex?
  • How do you convert 10111010₂ to hex?
  • Covert 3F2A₁₆ to binary.
  • What two ways can a negative number be represented in binary?
  • With n bits
    • How many different things again?
    • What is the range for sign-magnitude
    • What is the range for two's complement.
  • List all of the numbers for 4 bit two's complement
  • How do I represent -34 in 8 bit two's complement.
  • What is 100101₂ in decimal (assume 6 bit two's complement)
• Units, Dimensional Analysis
  • If you want to represent a lot of something, how do you do it?
  • Look at the Standard Prefixes for SI Units.
  • Or the lower right hand corner of the green card.
  • Unfortunately you will need these as well:

    Name	Symbol	Base 10
    milli	m	10-3
    micro	μ	10-6
    nano	n	10-9
    pico	p	10-12

  • A clock runs at 3.1 GHz, how long is the cycle.
    • Remember a Hz or Hertz is the SI unit if frequency.
      • Hz is a measure of cycles/second.
      • Hz is how we measure the speed of a clock.
    • Cycle length is the inverse of this, or seconds/cycle.
    • So the simple answer is 1/3.2GHz. But this is an unacceptable answer
      • Things should be in the proper units, so this should be in seconds per cycle, or just seconds.
      • Numbers should generally be between 1 and 100
      • But sometimes answers like .4 will do.
      • But never .00000000003412
    • And just an answer is not acceptable.
      • You must show your work
      • So you can check to see what you have done.
      • So others can check to see what you have done.
      • So you don't waste money.
      • So I can give partial credit.
      • Because I said so.
    • So

      1Hz = 1 cycle/sec
      1 GHz = 1x109cycles/sec
      
      So the answer is 
         1 sec/3.2x109cycles            
                                                            1/3.2 =  .3125
      	   = .31 x 10-9 sec/ cycle 
      	   = 310 x 10-12 sec/cycle     
      	                                              1012 ps = 1 sec
      					              so 1 = 1012ps/1 sec
                 = 310 x 10-12 sec/cycle x 1012ps/sec
                 = 310 x 10-12 sec/cycle x 1012ps/sec
      	   = 310 ps/cycle or 310 ps. 
                   
           
      	   

    • This is an acceptable form for a computation.
    • And if I can do it in HTML you can do it in word, latex, ...