In general terms duty cycle means proportion of time for which device is operated. In terms of square wave signal it defines the percentage of time for which signal is at logic high level. For square wave it can be calculated as (high time / (high time + low time))
Duty cycle of 50% means that the low time and high time of the signal is same.
Change of duty cycle is basic fundamental behind PWM. Serach for Duty cycle or PWM in google you will find lot of information about it.
The output of a device that has 2 conditions ie on off / high low must have a duty cycle relating to the percentage each one is active. A divece that has a duty cycle of 50% will be in one state and then the other state for exactly the same amount of time.
well, you can use this to make multiplication by other numbers
for instance: multiplying by 10 is multiplying by (8+2)
you can make three shifts for the 8
and one shift for the 2
and then add them
for instance: multiplying by 3 is multiplying by (2+1)
one shift for 2
no shift for 1
and then adding