1. Do the following base conversions. (10 pts) a. Convert the binary number 1101

Question

1. Do the following base conversions. (10 pts)

      a. Convert the binary number 110100 to decimal                                                          

      b. Convert the decimal number 94 to hexadecimal                    

      c. Convert the binary number 10111011 to hexadecimal                      

      d. Convert the hexadecimal number B3 to binary                            

      e. Convert the hexadecimal number 39E to binary                    

2. The Starship Enterprise is visiting a planet where the inhabitants have 7 fingers. Not surprisingly, they use a base 7 numbering system. The planet provides a beam-down coordinate of 5416 (in base 7). Translate this to base 10 so the crew can safely go on shore leave. (Hint: use place values) (5 pts)

3. An Ethernet frame contains 900 bytes of payload data. You will need to look up the length of the header and trailer. Calculate the percentage of the frame that is overhead (do not include the preamble in the frame). (5 pts)

4. Assume an Ethernet frame is to carry 30 bytes of payload data. What is the size of the frame in bytes? You will need to look up the length of the header and trailer. (do not include the preamble in the frame, but do include padding if necessary) (5 pts)

5. An ISP has CIDR block 134.103.128.0/17. The ISP wants to create 4 sub-blocks from this block. (5 pts)

a.How many bits should the ISP add to the mask for the subblocks?

b.What are the addresses (in dotted decimal, with the mask in slash format) for each subblock?

c.What is the maximum number of hosts in each subblock?

Explanation / Answer

1. Do the following base conversions. (10 pts)

a. Convert the binary number 110100 to decimal
0 * 2^0 + 0 * 2^1 + 1 * 2^2 + 0 * 2^3 + 1 * 2^4 + 1 * 2^5 = 0 + 0 + 4 + 0 + 16 + 32 = 52 base 10.
  
b. Convert the decimal number 94 to hexadecimal
94 / 16 = 5   with a remainder of 14 (E).
5 / 16 = 0   with a remainder of 5 (5).
So, 94 base 10 = 5E base 16.
  
c. Convert the binary number 10111011 to hexadecimal
1011 1011.
1011 in hexadecimal = B.
So, the number 10111011 base 2 equals BB base 16.
  
d. Convert the hexadecimal number B3 to binary
B's binary equivalent is: 1011.
3's binary equivalent is: 0011.
So, binary value is: 1011 0011.
  
e. Convert the hexadecimal number 39E to binary
3's binary equivalent is: 0011.
9's binary equivalent is: 1001.
E's binary equivalent is: 1110.
So, binary value is: 0011 1001 1110.

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