1.1. Data Representation

Question 1

The basis of any number system consists of:

Answer 1

• A base: the number of digits that a number system
  can use to represent numbers
• Place value for each digit: digits in certain positions
  have a specific value

Question 2

Denary

Answer 2

Base 10 integer digits

Question 3

Binary Systems

Answer 3

Base 2

Question 4

• kilo- (k)
• mega- (M)
• giga- (G)
• tera- (T)

Answer 4

• ×10^3
• ×10^6
• ×10^9
• ×10^12

Question 5

• kibi- (Ki)
• mebi- (Mi)
• gebi- (Gi)
• tebi- (Ti)

Answer 5

• ×2^10
• ×2^20
• ×2^30
• ×2^40

Question 6

Binary Coded Decimal (BCD)

Answer 6

• Binary representation where each positive denary digit is represented by a sequence of 4 bits (nibble)
• Only certain digits are converted to BCD, because particular digits represent a digit greater than 9.

Question 7

Practical applications of BCD

Answer 7

• A string of digits on any electronic device displaying
  numbers (eg. Calculators)
• Accurately measuring decimal fractions
• Electronically coding denary numbers

Question 8

Two’s Complement

Answer 8

• We can represent a negative number in binary by
  making the most significant bit (MSB) a sign bit, which
  indicates whether the number is positive or negative.
• Find the binary equivalent of the denary number
  (ignoring the -ve sign) | 42 = 101010

Flip all the bits | 00101001
Add 1 | 00101010
Convert binary to denary and put a –ve sign) | -42

Question 9

Maximum positive number in 8 bits

Answer 9

256

Question 10

Maximum negative number in 8 bits

Answer 10

-128

Question 11

Hexadecimal Systems

Answer 11

• Base 16
• Possible digits: 0 to 9 and A to F, where A to F
  represent denary digits 10 to 15

Question 12

Practical applications of Hexidecimal

Answer 12

• Defining colours in HTML
• Defining Media Access Control (MAC) addresses
• Assembly languages and machine code
• Debugging via memory dumps

Question 13

Character Sets

Answer 13

• A character set generally includes upper & lower case
  letters, number digits, punctuation marks and other
  characters.
• Character sets use different binary representations
  for each character via character encoding

Question 14

Character Encoding Standards

Answer 14

ASCII, Extended ASCII, Unicode

Question 15

ASCII

Answer 15

• Only English
  alphabets can be
  represented
• Each character
  encoding takes up
  7 bits, hence 128
  possible characters
• Smaller storage
  space.

Question 16

Extended ASCII

Answer 16

• ASCII’s extension -
  Also includes most
  European
  languages’
  alphabets
• ASCII extended to 8
  bits, hence 256
  possible
  characters

Question 17

Unicode

Answer 17

• Superset for ASCII
  & extended ASCII -
  recognized by
  various global
  languages
• Greater range of
  characters, as it
  uses 2 or 4 bytes
  per character.
• 2 or 4 times more
  storage space per
  character.