# 34 - Past Paper Simulation - Data Rep (A) #1

1. State the hexadecimal representation of the following binary pattern: 0100 0000 1110. (1 mark)

2. State the value of the binary pattern below as a decimal number if it represents a signed binary integer using two?s complement representation. 0100 0000 1110.(1 mark)

3. A two's complement floating point number is shown below. Fill in the blanks for 1 and 2 below. (2 marks) 4. Is the following floating point number normalised? How does the bit pattern indicate whether or not a number is normalised? (2 marks)
`Floating Point Number: 0.111111000 111111`

5. What is the largest positive value that can be stored in this floating point representation? Give your answer in Decimal. 6. A normalised floating point representation uses a 7-bit mantissa and a 5-bit exponent and both stored using two?s complement. In Binary, write the most negative number that can be represented in this format. (1 mark)

7. The following shows a floating point representation of a number. Calcuate the decimal equivalent of this number. State whether the number is negative or positive. (2 mark)
`Floating point representation of a number: 1010100 00110`

8. Write the normalised floating point representation of the denary value 416 with 7 bits for the mantissa and 5 for the exponent. (1 mark)

9. There are three different calculations that might cause an error to occur in a floating point system. (see the list below) List three different errors. (3 marks)
```Multiplying two very large numbers together.

Dividing a number by a very large number.

Adding together two numbers of very different sizes eg a tiny number to a very big number.	 ```

10. The below binary pattern represents a normalised two?s complement floating point number with an eight bit mantissa and four bit exponent. State its value in Decimal and state whether it is positive or negative. (2 marks)
`Normalised two's complement floating point number: 1001 1000 0100 `

11. Give one reason for storing floating point numbers in normalised form (1 mark)

12. Why are bit patterns often displayed using hexadecimal instead of binary? (1 mark)

13. Floating point numbers are usually stored in normalised form. State two advantages of using a normalised representation (2 marks)

14. Scientists working with normalised floating point numbers decide to increase the exponent's bit capacity from 3 bits to 5 bits. What will the effects of doing so be? (2 marks)

15. Explain what overflow is and give an example of a situation which might cause overflow to occur (3 marks)