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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