Working with clock frequencies and clock cycles.

  Decimal based.

  Basic unit is hertz  1 cycle/sec. 

   Common computer frequencies.
    Kilohertz (kHz) - 1*10^3 cycles/sec - analog modem speeds. 540-1611KHz (AM)
    Megahertz (MHz) - 1*10^6 cycles/sec - early cpu, bus speeds. FM radio.
    Gigahertz (GHz) - 1*10^9 cycles/sec - cpu processing speed.
      CPU 5 GHz 
      Transitor 700 GHz (room temp.)
      100 Gbps commerical fiber.

    Terahertz (THz) - 1*10^12 cycles/sec - fiber optics, optical transistors. 
      225 Tbits/sec.
      https://www.extremetech.com/extreme/192929-255tbps-worlds-fastest-network-could-carry-all-the-internet-traffic-single-fiber 

    Petahertz (PHz) - 1*10^15 cycles/sec 

  Individual clock cycles are expressed as fractions of a second.
    (1 Kilohertz) 
    millisecond (msec, ms) - 1*10^-3 seconds.
      (Modems)

    microsecond (u(mu)sec, us) - 1*10^-6 seconds. 
      (instruction speeds)

    nanosecond - (nsec, ns) - 1*10^-9 second 
    - steps in execution of single instruction or response time of gates on
      old systems.

    5280 ft/mi * 186,000 mi/sec = 982,080,000 ft/sec (speed of light)
      = electrons travel 1 ft/nsec  

    picosecond - (psec) - 1*10^-12 - size of binary pulses in fiber optics.
    - steps in execution of single instruction or response time of gates on
      modern systems.

    femtosecond - 1*10^-15 - laser pulses.
      pico and femto also appear when measuring the size of very small 
      capacitors (like ones used as memory cells in DRAM)

    attosecond - 1*10^-18 - nuclear reactions.  


Converting
   If cpu speed 1 GigaHertz, what is the length of each clock?
     1Hz = 1 cycle/sec.

     1 GHz     *     1*10^9 Hz / 1 GHz    *    (1 cycle/sec) / 1 Hz 
        = 1*10^9 cycles/sec.

     To determine length a cycle, divide 1 by clock speed.

     1/(1*10^9 cycles/sec)  =  1*10^-9 sec/cycle   *   1 ns / (1*10^-9 sec)
       = 1 ns/cycle.

   If cpu speed 4 GigaHertz, what is the length of each clock?
     1/(4*10^9) cycles/sec  = 1/4 * 10^-9 sec/cycle = .25 ns/cycle.
              .25 * 10^3 sec/cycle * 10^-12 sec/cycle =
                 250*10^-12 sec/cycle.  

   If cpu clock pulse is 4ns, what is the cpu speed?
     1ns. (nano-second) = 1 * 10^-9 second.
    so :
     1 /(4*10^-9 sec/cycle) = 1/4 * 10^9 cycles/sec 
     = .25 * 10^3 * 10^6 cycles/sec = 250 MHz 


  Works the same in the other direction.

   Given an instruction that executes in 8 ns.  8 ns/ins.

   8 ns/ins.  *  1*10^-9 sec./ns  = 8*10^-9 sec/ins.

   1 sec.  /   8*10^-9 sec/ins.   = 1/8 * 1/(10*^-9)  ins./sec
    # when a ratio of units appears under a division sign
    #   the units are flipped.
    # And the sign of a power is reversed.


   1/8 = .125 = 1.25 * 10^-1 

   1/(10^-9) = 10^9 


   1.25 * 10^-1 * 10^9 ins./sec  = 1.25 * 10^8 ins./sec

   1.25 * 10^2 * 10^6 ins./sec   = 125 * 10^6 ins./sec


Keep in mind that powers are powers of other powers.

  1000 Kilohertz = 10^3 * 10^3 = 10^6 = 1 Megahertz
  1 millisecond = 1^10-3 = 1^10^3 * 1^10^-6 = 1000 microseconds.