week04_soln.pdf - Mat1101 Tutorial Week 4 Bases and Number...

Mat1101 Tutorial Week 4
Bases and Number Representation
Grossman Chapter 3
1. Find the 16-bit computer representation of the following integers.
(a) 1880
(b) −1880 (c) 519 (d) −519 2. How do the representations in Question 1 change if the computer
uses 32-bits to represent integers?
(a) 1880
(b) −1880 (c) 519 (d) −519 3. Write the following binary numbers in normalised exponential
form.
(a) 111010011
2
(b) 0.00001110101
2

(c) 1101.001101
2
= 0.1101001101
2
× 2
4
(d) 111010011.00011010111
2
= 0.11101001100011010111
2
× 2
9
4. Assume that on a particular 16-bit computer, 7 bits are reserved
for the mantissa.
(a) Compute the exponent bias for this computer.
(b) Find the floating point (real) number computer representa-
tion of the four numbers given in Question 1 above.