F453 - data representations

Question 1

4 bits for mantissa
4 bits for exponent

calculate denary

i) 01010110
ii) 01001110

Answer 1

i)exponent 0110=6
mantissa 0.101
move 6 places to right becomes 0101000. value is 40
ii)1110= -2
mantissa 0.100
move 2 places left becomes 0.001
value is 1/8 (0.125)

Question 2

7 bits for mantissa
5 bits for exponent

which is normalised
p=101100110001
q=110100110011

Answer 2

P is normalised

starts with 10

Question 3

7 bits for mantissa
5 bits for exponent

write the normalised form for

0001101 00101

Answer 3

mantissa 0001101
move point 2 places right and fill with 0s on right
decrease exponent 2
01100100 00011