Question

1. The place values for the eight binary digits used in IPv4 addressing are as follows: 128, 64, 32, 16, 8, 4, 2, 1. Expand this range to include an additional four bits. Do this by recording the place values for 2¹¹, 2¹⁰, 2⁹, and 2⁸.
   
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2. Express the decimal value 2001 in binary by placing 1s in the binary positions requiring the addition of the corresponding place value. Place 0s in the binary positions where the corresponding place value should not be added. You should have 11 binary digits.
   
   
   
3. To express this binary number in hexadecimal, you must first group the 11 digits in sets of four. Because 11 is not evenly divisible by 4, begin by adding a leading zero to your binary number so that you have 12 binary digits. The decimal equivalent should still be 2001. It should not change because of the added leading zero. Record your binary 12-digit number below.
   
   
   
4. Group the 12 binary digits into three sets of four binary digits.
   
   
   
5. Convert each group of binary digits to a hexadecimal digit using Table 13-1. The result should be a three-digit hex number.
   
   
   

Table 13-1 Binary to hex to decimal conversion

Binary	Hexadecimal	Decimal
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
0111	7	7
1000	8	8
1001	9	9
1010	A	10
1011	B	11
1100	C	12
1101	D	13
1110	E	14
1111	F	15

6. Check your answer by multiplying the hexadecimal digits in your answer by their corresponding place value to get the decimal equivalent. For example: (3rd hex digit * 16²) + (2nd hex digit * 16¹) + (1st hex digit * 16⁰). Your decimal equivalent should equal 2001. Did you get the correct result? If not, double-check your decimal to binary and binary to hexadecimal conversions.
   
   
7. Next, try converting a hexadecimal number (CD4) to binary and then to decimal. First, treat each hexadecimal digit as four binary digits, using Table 13-1 as necessary. Record your answer below. You should have 12 binary digits grouped in three sets of four.
   
   
   
8. To convert the binary number recorded in Step 7, add the decimal place values of the 1’s binary digits. Record your answer below.
   
   
   
9. To double-check your answer, multiply the decimal value of each hexadecimal digit in CD4 with the corresponding place value, as you did in Step 6. Your answer should be 3284. Is your answer 3284? __________.
   
   
   
10. Why is the binary numbering system used in networking?
    
    
    
11. Why do we use hexadecimal representations of data instead of its binary equivalent?
    
    
    
12. Our decimal numbering system is base __________, the binary numbering system is base __________, and the hexadecimal numbering system is base ____________.
    
    
    
13. Why does it require fewer hexadecimal numerals than binary numerals to express any given number?
    
    
    

True or false? Some numbers are too large and cannot be expressed in binary.

Answer 1