A-level Computing 2009/AQA/Processing and Programming Techniques/Data Representation in Computers/Answers

Hexadecimal
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 * 1) Convert the following bases to their equivalent hexadecimal values
 * 2) $$8_{16}$$
 * 3) $$A_{16}$$
 * 4) $$10_{16}$$
 * 5) $$1_{16}$$
 * 6) $$5_{16}$$
 * 7) $$F_{16}$$
 * 8) $$AB_{16}$$
 * 9) $$1000\ 0000_2 \to 80_{16}$$
 * 10) $$0001\ 1101\ 0011\ 1101_2 \to 1D3D_{16}$$
 * 11) $$AF0BE_{16}$$
 * 12) Convert the following hexadecimal values to the given base
 * 13) $$14_{10}$$
 * 14) $$1110\ 0011_2$$
 * 15) $$0111\ 0011_2 \to 115_{10}$$
 * 16) $$1011\ 1110\ 1110\ 0101_2$$
 * 17) $$1011\ 1110\ 1110\ 1111_2 \to 48879_{10}$$
 * 18) $$426174_{16}$$
 * 19) 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?
 * 2) $$27$$
 * 3) $$-1$$
 * 4) $$125$$
 * 5) $$-103$$
 * 6) $$-72$$
 * 7) Convert the following numbers into negative numbers written in binary
 * 8) $$1111\ 1111$$
 * 9) $$1010\ 0000$$
 * 10) $$1000\ 0001$$
 * 11) $$0000\ 1100 \to 1111\ 0100$$
 * 12) $$0100\ 0011 \to 1011\ 1101$$
 * 13) $$0011\ 0111 \to 1100\ 1001$$
 * 14) $$0111\ 1110 \to 1000\ 0010$$
 * 15) Convert the following hexadecimal values to the given base
 * 16) $$-3$$
 * 17) $$-12$$
 * 18) Find the answers to the following sums in binary, show your working - not yet finished beyond here (YR 12 please complete!!)
 * 19) 0110 1100 - 0000 0111 = 01100101
 * 20) 0001 1111 - 0001 0011
 * 21) 0111 0111 - 0101 1011
 * 22) 23 (hex) - 1F (hex)
 * 23) 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?
 * 2) 0011.1000
 * 3) 0101.0111
 * 4) 0110.1100
 * EF
 * 1) 1001.0011
 * 2) 1100.1101 (note: this number is a two's complement number)
 * 3) 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
 * 4) 0001.1000
 * 5) 1000.1100
 * 6) 1001.0011
 * 7) 0000.1001
 * 8) 1101.1001 (as close as you can get)
 * 9) What are the values of the following 16 bit floating point numbers, where the exponent is 6 bits
 * 10) 0111 0100 1100 1110
 * 11) 0110 0000 0011 1010
 * 12) 1011 1100 0100 0001
 * 13) 1110 0000 0011 1101
 * 14) Normalise the following 16 bit floating point numbers, where the exponent is 6 bits
 * 15) 0011 0000 0000 0001
 * 16) 0001 1100 0000 1110
 * 17) 1101 0110 0100 0010
 * 18) 1111 0111 1111 1001