Binary Representation Worksheet
ASCII, Hexadecimal, and Binary Representations Worksheet
1. Consider the bit string 0011001010101101
a. In Unicode, this represents the symbol ㊭
b. In 16-bit floating point, this represents .6689453125×10-7
c. As a compact representation of a set, this would represent {3, 4, 7, 9, 11, 13, 14, 16}.
d. Convert the string to Hexadecimal
e. Convert the string to ASCII
2. What does each of the following bit strings represent in the various encodings?
| |ASCII |Hexadecimal |binary |2’s complement |excess |floating point |
|10110110 |N/A |B6 |182 |-74 |54 |- 3/16 |
|00111010 | | | | |-70 |5/16 |
|11111001 | | | | |121 |4.5 |
3. Perform the following conversions. Use 8 bits for 2’s complement. If a conversion is not possible, answer “N/A”.
|Base 10 |21 |255 |511 |-14 |
|Binary | | | | |
|2’s Complement | | | | |
4. Convert each of the following bit strings to base 10, assuming it is represented in binary and then 2’s complement. If a conversion is not possible, answer “N/A”.
|Bits |00101001 |00001101 |11111111 |01010011 |10000000 |
|As Binary |41 | | | | |
|As 2’s Complement |41 | | | | |
5. Perform the computations on the following two’s complement numbers, and indicate if overflow has occurred.
|(6-bit) | | | | |
| |001101 |111010 |001011 |001011 |
| |+101010 |+100110 |+101111 |+011111 |
|Answer | | | | |
|Overflow? | | | | |
|(8-bit) | | | | |
| |10011010 |00001011 |00111010 |10101011 |
| |+11010111 |+01101111 |+01100110 |+11100111 |
|Answer | | | | |
|Overflow? | | | | |
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