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

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1. Convert the following bases to their equivalent hexadecimal values
1. $8_{{16}}$
2. $A_{{16}}$
3. $10_{{16}}$
4. $1_{{16}}$
5. $5_{{16}}$
6. $F_{{16}}$
7. $AB_{{16}}$
8. $1000\ 0000_{2}\to 80_{{16}}$
9. $0001\ 1101\ 0011\ 1101_{2}\to 1D3D_{{16}}$
10. $AF0BE_{{16}}$
2. Convert the following hexadecimal values to the given base
1. $14_{{10}}$
2. $1110\ 0011_{2}$
3. $0111\ 0011_{2}\to 115_{{10}}$
4. $1011\ 1110\ 1110\ 0101_{2}$
5. $1011\ 1110\ 1110\ 1111_{2}\to 48879_{{10}}$
3. $426174_{{16}}$
4. Hexadecimal numbers are easier for humans to read, understand and remember.

## Negative Binary Numbers

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1. What are the denary values of the following twos complement numbers?
1. $27$
2. $-1$
3. $125$
4. $-103$
5. $-72$
2. Convert the following numbers into negative numbers written in binary
1. $1111\ 1111$
2. $1010\ 0000$
3. $1000\ 0001$
4. $0000\ 1100\to 1111\ 0100$
5. $0100\ 0011\to 1011\ 1101$
6. $0011\ 0111\to 1100\ 1001$
7. $0111\ 1110\to 1000\ 0010$
3. Convert the following hexadecimal values to the given base
1. $-3$
2. $-12$
4. Find the answers to the following sums in binary, show your working - not yet finished beyond here (YR 12 please complete!!)
1. 0110 1100 - 0000 0111 = 01100101
2. 0001 1111 - 0001 0011
3. 0111 0111 - 0101 1011
4. 23 (hex) - 1F (hex)
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. 0011.1000
2. 0101.0111
3. 0110.1100
4. EF
5. 1001.0011
6. 1100.1101 (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. 0001.1000
2. 1000.1100
3. 1001.0011
4. 0000.1001
5. 1101.1001 (as close as you can get)
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