Decimal is a Base 10 system with 10 possible values (0 to 9) and Binary is a Base 2 system with only two numbers 0 or 1.
i. Converting binary to decimal - The weightage of binary digits from right most bit position to the left most bit position is given below.
27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 |
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Example: Convert 10011101 into a decimal value.
There are eight bits in the binary number. The decimal value for each bit position is given below:
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | « Decimal equivalent of the binary position |
1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | « Given binary number |
To convert, you simply take a value from the top row wherever there is a 1 below, and then add the values together. For instance, in our example we would have
1*27 +
0*26 + 0*25 + 1*24 + 1*23 +
1*22 + 0*21 + 1*20
= 128 + 0 + 0 + 16 + 8 + 4 + 0+ 1
= 157 (decimal value)
ii. Converting decimal to binary
To convert decimal to binary is also very simple, you simply divide the decimal value by 2 and then write down the remainder, repeat this process until you cannot divide by 2 anymore.
For example, take the decimal value 157:
157 ÷ 2 = 78 with a remainder of 1
78 ÷ 2 = 39 with a remainder of 0
39 ÷ 2 = 19 with a remainder of 1
19 ÷ 2 = 9 with a remainder of 1
9 ÷ 2 = 4 with a remainder of 1
4 ÷ 2 = 2 with a remainder of 0
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1 <--- to convert, write this remainder first
Next write down the value of the remainders from bottom to top (in other words write down the bottom remainder first and work your way up the list) which gives: 10011101 = 157
Example: What is the possible decimal equivalent of 10101010?
Position of Bit | 7th | 6th | 5th | 4th | 3rd | 2nd | 1st | 0th |
Decimal Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Calculate the decimal equivalent based on the above predefined values.
Given Binary Number is: 10101010, it's decimal equivalent is:
1*(2^7) + 0*(2^6) + 1*(2^5) + 0*(2^4) + 1*(2^3) + 0*(2^2) + 1*(2^1) + 0*(2^0)=170 in decimal format.
Specify the static route on the device to resolve and determine the packet's next-hop interface using the Longest Match Routing Rule (most specific entry), sometimes referred to as the longest prefix match or maximum prefix length match. The Longest Match Routing Rule is an algorithm used by IP routers to select an entry from a routing table. The router uses the longest (prefix) match to determine the egress (outbound) interface and the address of the next device to which to send a packet. Typically, the static route prefers the directly connected subnet route for resolving the next hop rather than performing a longest prefix match with any other available routes.
The router implements the Longest Match Routing Rule as follows:
Longest Match Example:
The router receives a packet with a destination IP address of 192.168.1.33.
The routing table contains the following possible matches:
192.168.1.32/28 ,192.168.1.0/24,192.168.0.0/16