“Question 2 (20 marks) This question allows you to demonstrate your ability to work with the different number bases associated with this module. In every case you must show your working to gain full marks. By all means use a calculator to check that your answers are correct, but it will be very useful for you to be able to manipulate these types of numbers without using a calculator. a) Convert each of the following binary numbers (in dotted binary form) to dotted decimal as shown in the Cisco Academy Network Fundamentals online material in Chapter 6. Remember to show your working. b) Find the decimal result of ANDing the two decimal numbers shown in each of the following pairs. Remember to show your working for the decimal/binary conversion, the binary/decimal conversion and the AND function. The AND function has the following properties: If the two compared values are both 1, the result is 1. If one of the values is 0 and the other is 1, the result is 0. If both of the compared values are 0, the result is 0.”

In each of the conversions below, the binary octets of the 32 digit dotted binary number can be converted into a decimal number as outlined below in the individual tables.  The final 4 decimal numbers of each conversion are then joined using a decimal dot between the numbers to give a final dotted decimal value.

i)  11111111.11111111.11111100.00000000

[Table]

Hence:

128 + 64 + 32 + 16 + 8 + 4 + 2 +1 (= 255). 128 + 64 + 32 + 16 + 8 + 4 + 2 +1 (= 255). 128 + 64 + 32 + 16 + 8 + 4 + 0+0 (= 252). 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 (= 0)

Dotted decimal  format = 255.255.252.0

ii)  00001010.11001000.00110010.01100100

[Table]

Dotted decimal format =  10.200.50.100 …(short extract)

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