Refer to the following binary number when answering the questions below 01000000

Question

Refer to the following binary number when answering the questions below 0100000000110000 How many bytes does this number require? (Write just a number in the blank.) What decimal number does this binary number represent? (Write just a base 10 number in the blank with no commas.) What hexadecimal number does this binary number represent? (In the blank, write a hexadecimal number with lowercase letters, as few digits as possible, and no leading "Ox") What text would this binary number represent, assuming it uses ASClI encoding? (In the blank, write just the letters this number would encode.) Suppose you changed the leading digit to a 1. What decimal number would the resulting binary number represent, assuming it uses sign-magnitude format? (Your answer should be a negative base 10 number with no commas.) Suppose the leading digit is still a 1 instead of a 0. What decimal number would the resulting binary number represent, assuming it uses two's complement format?(Your answer should be a negative base 10 number with no commas.) Suppose the leading digit is a 0 again, and you added 16 more zeros at the end of the binary number. What decimal floating point number would the result represent? (Write a floating point number in base 10 in the blank.

Explanation / Answer

1. 2 bytes ( 01000000 00110000 = 16 bits)

2. decimal number equivalent = 24 + 25 + 214 = 16432

3. Hexadecimal Equivalent

   remainder

2| 16432

2| 1027 0

2| 64 3

2|4 0

2|0    4

= (4030)16

4. ASCII code

40 = @

30 = 0

4030 = @0

5. 1 100000000110000 = -16432 ( 1 at most significant position represents negative number)

6. 2's complement

1100000000110000

1's complement = 0011111111001111

2's complement = 1's complement + 1= 0011111111010000 = -16336

7. 0100000000110000 0000000000000000

= 269221888.0000

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