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Data Representation and Data Types (Describe the following different…
Data Representation and Data Types
Explain the terms bit, byte and word
A
bit
is a
single binary digit
, for example 1or a 0.
A
byte
is a
collection
of
8 bits.
A
word
is the
total number of bits
that can be manipulated as a
single unit
by the CPU.
Describe and use the binary number system and the hexadecimal notation as shorthand for binary number patterns
Denary
is
base 10
(our number system).
Binary
is
base 2
- each column from right to left is multiplied by 2.
Hexadecimal
:
0-9 are numbers, 10-15 are A-F.
Why is Hex used to represent binary numbers?
It
acts as a shorthand
for binary.
It
requires fewer characters
than binary.
Describe how characters and numbers are stored in binary form / Describe standardised character sets
Standardised Character Sets
-
each character is mapped to a binary number.
This ensures that
computers use the same character representation
and can transfer
meaningful data.
Unicode
Advantages - can
represent a larger range of characters
than ASCII; allows the
storage of complex characters
such as Chinese symbols and emojis.
ASCII (American Standardised Code Information Interchange)
Follow this link for an explanation of how ASCII represents uppercase and lowercase characters in binary:
https://drive.google.com/file/d/1O22n6D6UEB4vPyHLFURl-mo__d_sp-Xg/view?usp=sharing
Explain the representation of positive and negative integers in a fixed-length store using both two's complement, and sign and magnitude representation. / Apply binary arithmetic techniques.
See 2.3 2 PowerPoint
Describe the following different primitive data types, Boolean, character, string, integer and real. / Describe the storage requirements for each data type.
Character - 1 byte
String
- one byte per character
Boolean
- one bit - 0 or 1
Integer
- 1 byte (0 to 255), 2 bytes (0 to 65535)
Real
- one byte for whole number and one byte for decimal.
Describe truncation and rounding and their effect upon accuracy
Truncation
Number is
approximated
to the nearest whole number/tenth/hundredth
nearer zero
. (The number is cut off)
Rounding
Number is
approximated
to the nearest whole number/tenth/hundredth
Both rounding and truncating cause
inaccuracy
if the results are used in
further calculations
. Also, a
test for equality
might fail if a
minor difference
is caused by
rounding
.
Absolute error
is the
positive or negative difference
between the original value and the answer.
Relative error
is 100 divided by the original number multiplied by the difference. It's expressed as a
percentage
and can be
positive or negative.
State the advantages and disadvantages of representing numbers in integer and floating point forms. / Describe the nature and uses of floating point form
Integer
Advantages
: numbers are stored accurately; less complex processing; exact representation of zero.
Floating-point
Advantages
: very large/small numbers can be stored; larger range of numbers can be represented; fractions/decimals can be represented.
Convert between real number and floating point form
See 2.3 3 PowerPoint