Data Representation Covering… Binary addition / subtraction 2’s complement Floating Point Binary Normalisation of Floating Point Binary

Question 1 Question… Convert the 10001100 8-bit binary numbers to its denary equivalent. Answer… 140

Question 2 Question… Convert 67 denary to its 8 bit binary equivalent… Answer… 01000011

Question 3 Convert the 8-bit two’s complement binary 10000010 to its denary equivalents. Answer… -126

Question 4 Question… Convert -120 denary to its 2’s complement 8-bit binary equivalent Answer… 10001000

Question 5 Question… Convert 175 denary to its hexadecimal equivalent Answer… af

Question 6 Question… Convert BB hexadecimal to its denary equivalent Answer… 187

Question 7 Question… Convert 9B hexadecimal to its 8-bit binary equivalent Answer… 10011011

Question 8 Question… Convert the 8 –bit binary 10101010 to its hexadecimal equivalent Answer… aa

Question 9 Question… Represent 5.125 as a binary fraction Answer… 0101.0010

Question 10 Question… 1101000.011 What is the decimal equivalent? Answer… 104.375

Question 11 Question… What is 01101011 + 00100100 Answer… 10001111

Question 12 (2 marks) Question… What is 76 – 24 in 2’s complement 8-bit binary (show working for 1 mark and right answer for 1 mark) Answer… 76-24=52 01001100 11101000 00110100

Question 13 (2 marks) Question… What is -86 + 96 in 2’s complement 8-bit binary (show working for 1 mark and right answer for 1 mark) Answer… -86+96=10 10101010 01100000 00001010

Question 14 (3 marks) Question… The following floating binary numbers have a 10 bit 2’s complement mantissa and 6 bit 2’s complement exponent. What is the decimal value? a) 01001.01000 000100 4 b) .00101000000 111110 -2 c) 1100.11000 000011 3 Answer… a) 9.25 b) 0.15625 c) -3.25

Question 15 Question… What is the trade off when changing the size of the mantissa and exponent in terms of accuracy and range. Answer… A larger mantissa means higher accuracy and lower range whereas higher exponent means higher range but lower accuracy

Question 16 Question… Represent the value −0.3125 in floating point form using 10-bit two’s complement mantissa and 6-bit two’s complement exponent in normalised form. Answer… 1011000000 111111