Data Representation
Binary – base two number system based on the values 0 and 1 only.
Prefixes
Converting from binary to denary and from denary to binary
Example：
a) binary: 1 1 1 0 1 1 1 0
denary: 128 + 64 + 32 + 8 + 4 + 2 = 238 (denary)
b) the conversion of the denary number, 107, into binary
Binary addition and subtraction
one’s complement - each digit in the binary number is inverted (in other words, 0 becomes 1 and 1 becomes 0).
For example, 0 1 0 1 1 0 1 0 (denary value 90) becomes 1 0 1 0 0 1 0 1 (denary value −90).
two’s complement - each digit in the binary number is inverted and a ‘1’ is added to the right-most bit. (left-most bit, most significant bit, MSB)
For example, 0 1 0 1 1 0 1 0 (denary value 90) becomes:
1 0 1 0 0 1 0 1 + 1 = 1 0 1 0 0 1 1 0
(since 1 + 1 = 0, a carry of 1) = denary value −90
Overflow – the result of carrying out a calculation which produces a value too large for the computer’s allocated word size.
Hexadecimal number system
a system based on 16 different digits, the numbers 0 to 9 and the letters A to F, four binary digits are equivalent to each hexadecimal digit.
Practical applications:
1.Defining colours in HTML 2.Debugging via memory dumps
3.Defining Media Access Control (MAC) addresses
4.Assembly languages and machine code 5.IP addresses(IPv6)
Binary-coded decimal (BCD) system
binary-coded decimal (BCD) system uses a 4-bit code to represent each denary digit
Exercise 1
State two benefits of using Binary Coded Decimal (BCD) to represent values.[2]
Answer:
• straightforward to convert to / from BCD and denary
• ... so it is less complex to encode and decode for programmers
• easier for digital equipment use BCD to display output information
• can represent monetary货币 values exactly
Exercise 2
Identify one practical application of BCD and justify why BCD is used in this application.[2]
Character Set
ASCII codes and Unicodes
The standard ASCII code character set consists of 7-bit codes (0 to 127 denary or 0 to 7F in hexadecimal)
this represents the letters, numbers and characters found on a standard keyboard together with 32 control codes.
Extended ASCII uses 8-bit codes (128 to 255 in denary or 80 to FF in hex). This allows for non-English characters and for drawing characters to be included.
Unicode allows characters in a code form to represent all languages of the world (Huffman coding)
Exercise:
Answer:
Similarity (max 1):
• both can use 8 bits • both represent each character using a unique code
• Unicode will contain all the characters that ASCII contains // ASCII is a subset of Unicode
Differences (max 2):
• Unicode can go up to 32 bits per character whereas ASCII is 7 or 8 bits
•Unicode can represent a wider range of characters than ASCII
• different languages are represented using Unicode, ASCII is only for one language