How many digits would we need to represent the values 18, 789, and 10956 in binary?
 

Value

Formula

 

 

 

 

Digits Needed

18   

 log (18)
  log (2)

=

1.255
 0.301

=

4.048

5

789   

log (789)
  log (2)

=

2.897
 0.301

=

9.345

10

10,956  

log (10956)
  log (2)

=

4.040
 0.301

=

13.031

14

We could also have found the answer since we know 24 = 16, 25 = 32, and 29 = 512, 210 = 1024, and 213 = 8192, 214 = 16384.