Data Representation

Computer and Information Technology – Core Module – Data Representation

Computer & Information Technology Data Representation Common Number System: System Name Decimal / Denary

Base 10

Number used 0–9

Remark Human understandable

Binary

2

0, 1

Employed by computer

Hexadecimal

16

0–9

Usually used as a shorter way to represent binary numbers

A (11) – F (15)

Conversions between different number systems: 1. Decimal → Binary Convert 3410 to binary number 2 34 … 2 17 … 0 2 8 … 1 2 4 … 0 2 2 … 0 1 … 0 3410 = 1000102.

2.

Binary → Decimal Convert 1011012 into denary number 25 24 23 22 21 ↓ ↓ ↓ ↓ ↓ 1 0 1 1 0 1011012 = 25 + 23 + 22 + 1= 4510

3.

Decimal → Hexadecimal Convert 350810 into hexadecimal number 1 3508 … 6 1 219 …4 6 1 13 (D) … 11 (B) 6 350810 = DB416.

1 ↓ 1

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Computer and Information Technology – Core Module – Data Representation

4.

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Hexadecimal → Decimal Convert 2A36C2 into denary number 164 163 162 161 ↓ ↓ ↓ ↓ 2 A(10) 3 6

1 ↓ C(12)

2A36C16 = 2 × 164 + 10 × 163 + 3 × 162 + 6 × 161 + 12 = 17290810

5.

Binary ←→ Hexadecimal Binary 0000 0001 0010 0011 0100 0101 0110 0111

Decimal 0 1 2 3 4 5 6 7

Hexa 0 1 2 3 4 5 6 7

Binary 1000 1001 1010 1011 1100 1101 1110 1111

Decimal 8 9 10 11 12 13 14 15

Hexa 8 9 A B C D E F

(a) Convert 1010011012 into hexadecimal number. 1 0100 11012 = 0001 0100 11012 = 14D16

(b) Convert 5E2D16 into binary number. 5E2D = 0101 1110 0010 11012 = 1011110001011012

Important Numbers and Formulas 1. 27 = 128 28 = 256 210 = 1024 216 = 65536 2. 10……02 (n zeroes) = 2n. e.g. 1000000002 = 28 = 256 3. For n-bits unsigned integers: Minimum number = 00……0 (n zeroes) = 0 Maximum number = 11……1 (n ones) = 2n – 1 e.g. For 8-bits unsigned integers: Minimum = 00000000 = 0 Maximum = 11111111 = 28 – 1 = 255 * If a number requires more than the available number of bits, overflow will occurs. The leftmost bits will be removed.

Computer and Information Technology – Core Module – Data Representation

Memory Unit 1. Bit BInary digiT  Basic unit for storing data in computer  1 bit = 1 binary digit (i.e. 0, 1)  2. Byte Smallest addressable data in the microprocessor  1 Byte = 8 bits  3. Measurement units of data Unit 1 Kilobyte (1KB) 1 Megabyte (1MB) 1 Gigabyte (1GB) 1 Terabyte (1TB)

*

a. b.

Value 210 bytes 210 KB = 220 bytes 210 MB = 230 bytes 210 GB = 240 bytes

We use “B” to stand for “byte”, “b” to stand for “bit” When memory size is discussed, we usually use 2 as the base.

Character Coding Systems / Character Sets (Charsets) 1. ASCII 8 bits for each character  Printable characters + Non-printable (control and communication) codes  “0” – “9”: 48 – 57  “A” – “Z”: 65 – 90 “a” – “z”: 97 – 122 2. Big-5 Code 16 bits for each character  Mainly used to represent Traditional Chinese characters (繁體中文)  3. GB Code 16 bits for each character  Mainly used to represent Simplified Chinese characters (簡體中文)  4. Unicode 16 bits  International standard code  Support characters from different languages, including Traditional and  Simplified Chinese characters Increasing degree of recognition in different systems  * Conversion is needed to read characters from one charset to another.

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