A-level Computing/AQA/Processing and Programming Techniques/Data Representation in Computers/Questions

This page contains questions to assist the reader in understanding the course material. These questions should not be taken as an indication of examination questions, and the reader should make reference to previous exams to get an idea of these.

Hexadecimal

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1. Convert the following bases to their equivalent hexadecimal values
   1. 8 dec
   2. 10 dec
   3. 16 dec
   4. 0001 bin
   5. 0101 bin
   6. 1111 bin
   7. 1010 1011 bin
   8. 128 dec
   9. 7485 dec
   10. 1010 1111 0000 1011 1110 bin
2. Convert the following hexadecimal values to the given base
   1. E - decimal
   2. E3 - binary
   3. 73 - decimal
   4. BEE5 - binary
   5. BEEF - decimal
3. The binary value of the ASCII word Bat is $01000010\ 01100001\ 01110100_{2}$. What is the hexadecimal equivalent?
4. Why is hexadecimal used on computer displays instead of decimal or binary?

Negative Binary Numbers

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1. What are the denary values of the following twos complement numbers?
   1. 0001 1011
   2. 1111 1111
   3. 0111 1101
   4. 1001 1001
   5. 1011 1000
2. Convert the following numbers into negative numbers written in binary
   1. 0000 0001
   2. 0110 0000
   3. 0111 1111
   4. 12 (denary)
   5. 67 (denary)
   6. 34 (hexadecimal)
   7. 7E (hexadecimal)
3. Convert the following negative binary numbers into decimal
   1. 1111 1101
   2. 1111 0100
4. Find the answers to the following sums in binary, show your working
   1. 0110 1100 - 0000 0111 = 0110 0101 => 101
   2. 0001 1111 - 0001 0011 = 0000 1100 => 12
   3. 0111 0111 - 0101 1011 = 0001 1100 => 28
   4. 23 (hex) - 1F (hex) = 0000 0100 => 4
   5. 0001 0010 - 1111 1101 =

Binary Fractions

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1. What are the values of the following numbers where there are 4 numbers before the decimal point?
   1. 00111000
   2. 01010111
   3. 01101100
   4. EF
   5. 10010011
   6. 11001101 (note: this number is a two's complement number)
2. Using 1 byte for each number, with a fixed unsigned decimal point between bits 4 and 5, convert the following denary/decimal numbers into binary or get as close as you can
   1. 1.5
   2. 8.75
   3. 9.1875
   4. 0.5625
   5. 13.60
3. What are the values of the following 16 bit floating point numbers, where the exponent is 6 bits
   1. 0111 0100 1100 1110
   2. 0110 0000 0011 1010
   3. 1011 1100 0100 0001
   4. 1110 0000 0011 1101
4. Normalise the following 16 bit floating point numbers, where the exponent is 6 bits
   1. 0011 0000 0000 0001
   2. 0001 1100 0000 1110
   3. 1101 0110 0100 0010
   4. 1111 0111 1111 1001