Solutions8
Computer Architecture
Tutorial 4 – Floating Point Numbers
1) Convert the following decimal numbers to binary: a) 5.5 b) 8.25 c) 9.3 d) 11.46875
2) Convert the binary number 1001.1010101 to decimal.
3) Normalise the following binary numbers: a) 101.1 b) 1000.01 c) 0.00010101
4) Convert –31.3 to IEEE Single Precision format.
5) Interpret the 32-bit hexadecimal value C154 0000 as an IEEE Single Precision number.
6) Carry out the operation 31.3 + 13.25 in IEEE Single Precision arithmetic
7) Fill in the missing entries
Fraction Binary Decimal
1/4 0.01 0.25
3/8
23/16
10.1101
1.011
5.625
3.0625
8) Consider a five-bit floating representation based on the IEEE floating point format with 1 sign bit, two exponent
bits and 2 significand bits. For this format fill in the missing entries:
Bits Binary Value
or Special Value
Decimal value
or Special Value
0 00 00
0 00 01
0 00 10
0 00 11
0 01 00
0 01 01
0 01 10
0 01 11
0 10 00
0 10 01
0 10 10
0 10 11
0 11 00
0 11 01
0 11 10
0 11 11