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Data types Homework 4
Data types
Subject
Computer Science
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• A2 - A LevelAcademic year: 2023/2024
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point arithmetic
1
Homework 4 Floating point arithmetic
1. A certain computer holds floating point binary numbers using an 8 bit mantissa and a 4-bit
exponent.
(a) Convert the following numbers from floating point binary to denary.
(i) 0 0011 [2]
(ii) 1 0101 [2]
(b) Convert the following numbers from denary to normalised floating point binary.
(i) 13 [2]
(ii) -13 [2]
2. (a) What is the purpose of normalising a floating point binary number? [2]
(b) What is the most negative number that can be held in an 8-bit mantissa and a 4-bit
exponent, expressed as a decimal number? [2]
3. Numbers are stored in a computer system using fixed point binary with 5 places before and
7 places after the binary point.
(a) What is the maximum value that can be held, to the nearest whole number? [1]
(b) Explain what is meant by underflow. Describe a situation in which it could occur. [2]
101 exp = 3
.. 5.
10100 exp
= 5
.. - 20.
= 1101.
= 01101010 0010
10010110 0010
Reduce size taken and improve accuracy.
- 128
127
When the value is too small tobe expresed in the
number ofbits.
Ifa number less than - 128 is tried, underflow will occur.
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Data types Homework 4
Subject: Computer Science
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• A2 - A LevelWas this document helpful?
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mework 4 Floating point arithmetic
s
1
Homework 4 Floating point arithmetic
1. A certain computer holds floating point binary numbers using an 8 bit mantissa and a 4-bit
exponent.
(a) Convert the following numbers from floating point binary to denary.
(i) 0.1011100 0011 [2]
(ii) 1.0101101 0101 [2]
(b) Convert the following numbers from denary to normalised floating point binary.
(i) 13.25 [2]
(ii) -13.25 [2]
2. (a) What is the purpose of normalising a floating point binary number? [2]
(b) What is the most negative number that can be held in an 8-bit mantissa and a 4-bit
exponent, expressed as a decimal number? [2]
3. Numbers are stored in a computer system using fixed point binary with 5 places before and
7 places after the binary point.
(a) What is the maximum value that can be held, to the nearest whole number? [1]
(b) Explain what is meant by underflow. Describe a situation in which it could occur. [2]
101.11
exp
=
3
..
5.75
10100.11
exp
=
5
..
-
20.75
=
1101.01
=
01101010
0010
10010110
0010
Reduce
size
taken
and
improve
accuracy.
-
128
127
When
the
value
is
too
small
to
be
expresed
in
the
number
of
bits.
If
a
number
less
than
-
128
is
tried,
underflow
will
occur.