Metric Prefixes and Hertz

Notes

• We need some semi-specialized "mathy" things.
• We tend to measure very large and very small things.
  • Clocks run in the billions of cycles per second.
  • We tend to have trillions or more bytes of storage
  • instructions take less than 1x10^-9 seconds to complete
• To make it easier to compute, we tend to use the Metric Prefix system.
  • Look this up on Wikipedia.
  • There is the base unit, say byte
  • There are units for larger collections

    Name	Symbol	Conversion Factor
    kilo	k	1000, 103
    mega	M	106
    giga	G	109
    tera	T	1012
    peta	P	1015

    • There are larger units as well, exa, zetta, yotta, ronna, quetta but we are less likely to use these.
    • So 1x10⁹ bytes = 1 GB
    • We tend to like things in the 1- 999 value range
    • So 1,000,000 bytes is bad, but 1 gigabyte is acceptable.
  • And there are smaller units

    Name	Symbol	Conversion Factor
    mili	m	1000, 10-3
    micro	μ	10-6
    nano	n	10-9
    pico	p	10-12

    • Again we like numbers in the 1-999 range,
    • if something takes .001 seconds, we say it takes 1 ms

      .001 seconds = 1x10-3 seconds
                                         1 ms = 1x10-3s
      
                                 1 ms
                   =  1x10-3s x -------- 
                                 1x10-3s
      
                                 1 ms
                   =  1x10-3s x -------- 
                                 1x10-3s
      
                   = 1 ms
                  

    • Do I need to show that work?
    • Well, but don't goof it up.
    • And we will probably be in the middle of a larger computation
    • So just put it down.
    • I often goof up the wiggle the decimal point method.
• Bytes, kilobytes and kibibytes.
  • This is pedantic and does not matter in most of the rest of the world.
  • Technically a kilo is 10³ of the base unit.
  • But because the base 2 is so embedded in the computing world, we used 2¹⁰

  • n : k	10n	2k	10n/2k
    3 : 10	1,000	1024	.9766
    6 : 20	1,000,000	1,048,576	.9537
    9 : 30	1,000,000,000	1,073,741,824	.9312
    12 : 40	1,000,000,000,000	1,099,511,627,776	.9095

    There was a lawsuit
    Plus some general unhappiness with the inaccuracy
    So the multiple-byte units were introduced.

    Name	Symbol	Conversion Factor
    kibibyte	KiB	1024, 210
    mebibyte	MiB	220
    gibibyte	GiB	230
    tebibyte	TiB	240
    pebibyte	PiB	250

• Hertz (Hz)
  • 1 Hz is 1 cycle/ second
  • Or 1 event per second.
  • A normal clock "ticks" at 1 Hz
  • This is a measure of frequency
  • it is expected that you will use metric prefixes with this unit
  • So 1 kHz is 1000 events per second.
  • Modern clocks are measured in GHz units.
    • Apparently the Intel Core i9 processor 14900KS is the current highest clock rate processor that Intel makes.
    • see https://www.intel.com/content/www/us/en/products/sku/237504/intel-core-i9-processor-14900ks-36m-cache-up-to-6-20-ghz/specifications.html (no link as the page does not pass the wave test.)
    • It runs at 6.2GHz
• For clocks we care about:
  • The frequency or how often it "ticks" every second
    • Measured in Hertz
  • The period or how long a single "tick" takes.
    • Measured in seconds.
  • (Mattias Campe, via Wikipedia)
  • In this image
    • The clock rates are 1Hz, 2Hz and 3Hz.
    • The periods are 1 second/cycle, 1/2 second/cycle, 1/3 second/cycle
  • Notice that the period and frequency are inverses
  • < pre> 2 cycles 2Hz = -------- 1 second The inverse is 1 second -------- or 1/2 second/cycle 2 cycles
  • Some versions of the Arduino Nano have a 16MHz clock. How long is each clock cycle.

     Since the clock speed is 16MHz
     I have MHz
     I want seconds/cycle
                1x106 cycles
     16 MHz =   ------------
                1 second
    
    So a single cycle lasts
     
                1 second
                ------------
                1x106 cycles
    
                = 1/16 x 10-6 seconds / cycle
    
    At this point we will drop the /cycle, as that is what we are discussing
                = .0625 x 10-6 seconds
                = 62.5 x 10-9 seconds
    
       I am not allowed to talk about 10-9 seconds
       so 1 second = 109 nanoseconds (ns)
              
                                        1 x 109 ns 
                = 62.5 x 10-9 seconds x ------------
                                        1 second 
    
                = 62.5 ns (per cycle)
                

• You will frequently need to think about
  • What are the conversion units I need.
  • What "side up" do I want the fraction
• On your own, Find the speed of your processor and compute the length of time for each cycle. This will most likely yield an answer in the picosecond range.