Question

1. You are to create 17 subnets on a class B network with the IP address: 172.20.112.1? How many bits do you need to uniquely identify each subnet? (focus on the binary representation more so than the networking aspect of the question) : hint what is the minimum number of bits do you need to represent 17 different entities. (show all steps)
2. Subtract 10 – 7 using 2’s complement (show all steps)

3. Find the two’s complement of the following number:   10110111(show all steps)

9. Subtract 10 – 7 using 2’s complement (show all steps)

Answer 1

Given class B IP address 172.20.112.1

In class B, 16 bit are used for network and remaining 16 bits are used for host.

Now using 1 bit we can create 2 subnets, (0,1)

using 2 bits we can create 4 subnets (0,1,2,3)

using 4 bits we can create 16 subnets (0,1,2,.........15) (<17)

using 5 bits we can create 32 subnets (0,1,..........31) (>=17)

So we need to borrow 5 bits from host.

Subtract 10 – 7 using 2’s complement

To substract 7 from 10 we have to add 2's compliment of 7 to 10.

Binary of 10 = 1010

Binary of 7 = 0111 1's compliment of 7 = 1000 To get 2's compliment, we have to add 1

so 2's compliment of 7 = 1001

1010

+1001

10011

We got carry above. We can discard the carry and the remaining number is our result which is 3

Find the two’s complement of the following number:   10110111(show all steps)

To get two's compliment we have to find 1's compliment and add 1 to it.

1's compliment can be obtained by interchanging 0 with 1 and 1 with 0

1's compliment of 10110111 = 01001000

add 1 now

01001000

+ 1

01001001

so 2's compliment of 10110111 is 01001001