0110.  Without actually converting the numbers 84, 137, and 693 into binary, what can we predict about how the numbers will appear in binary?

 

84:  We know that it will require 7-bits (since 26 = 64 and 27 = 128)

We know that the right-most bit will be ‘0’ (since the number is even)

Of course, we know that the left-most bit will be ‘1’

 

137:  We know that it will require 8-bits (since 27 = 128 and 28 = 256)

We know that the right-most bit will be ‘1’ (since the number is odd)

Of course, we know that the left-most bit will be ‘1’

 

693:  We know that it will require 10-bits (since 29 = 512 and 210 = 1024)

We know that the right-most bit will be ‘1’ (since the number is odd)

Of course, we know that the left-most bit will be ‘1’