Show your work in writing up answers to the following questions to get full cred

Question

Show your work in writing up answers to the following questions to get full credit. rithm that was seen in class. 2. Convert positional notation 6.7510 from decimal to binary and hexadecimal using algo- rithms that were seen in class. 3. Convert positional notation 1FA.UO6G2 from base 32 to binary and then to hexadecimal. Here, much like base 16, we use letters A through V to represent 10 through 31, and note the fractional part in this case is U zero six G (i.e., it is difficult to see the difference between 0 and o). Use the shortcut of grouping binary bits as seen in class.

Explanation / Answer

Question 1

(0.101011)2 from binary to decimal

0.1 0 1 0 1 1

= 1*2^-1 0*2^-2 1*2^-3 0*2^-4 1*2^-5 1*2^-6

= 1*0.5+0+1*0.125+0+1*0.03125+1*0.015625

= 0.5+0.125+0.03125+0.015625

= (0.671875)10

Question 2

(6.75)10 from decimal to binary and hexadecimal

For 6

THe equivalent binary is 0110

FOr 0.75

0.75 * 2 = 1.5

0.5 * 2 = 1.0

The equivalent binary is 110

The final result is (110.110)2

The equivalent hexadecimal is (6.C)16

Question 3

1FA.U06G

(11510.310616)32

For 11510

11510 / 2 result 5755 remainder 0

5755 / 2 result 2877 remainder 1

2877 / 2 result 1438 remainder 1

1438 / 2 result 719 remainder 0

719 / 2 result 359 remainder 1

359 / 2 result 179 remainder 1

179 / 2 result 89 remainder 1

89 / 2 result 44 remainder 1

44 / 2 result 22 remainder 0

22 / 2 result 11 remainder 0

11 / 2 result 5 remainder 1

5 / 2 result 2 remainder 1

2 / 2 result 1 remainder 0

1 / 2 result 0 remainder 1

For 0.310616

2 * 0.310616=0.621232

2*.621232=1.242464

2*.242464=0.484928

2*.484928=0.969856

2*.969856=1.939712

2*.939712=1.879424

2*.879424=1.758878

2*.758878=1.517756

2*.517756=1.035512

2*.035512=0.071024

2*.071024=0.142048

2*.142048=0.284096

(11510.310616)32 = (10110011110110.10011111000)2

For hexadecimal (0010 1100 1111 0110.0100 1111 1000)2

(2CF6.4F8)16

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