Encoding Schemes and Number System

2.1 INTRODUCTION

This section introduces the fundamental concept of encoding schemes and number systems as used in computers. It begins by posing a question about how the keys on a computer keyboard, which are in human-recognizable form such as alphabets and symbols, are interpreted by the computer system. Since computers understand only binary language composed of 0s and 1s, every key pressed on the keyboard is internally mapped to a unique code value, which is then converted into its equivalent binary form for the computer to process. For example, pressing the key 'A' is internally mapped to the decimal value 65, which is then converted to its binary equivalent 1000001. Similarly, pressing the Hindi character 'ज' on a Hindi keyboard maps to a hexadecimal value 0905, whose binary equivalent is 0000100100000101. This process of converting data into an equivalent cipher using a specific code is called encoding. Encoding is crucial because it standardizes how textual data is represented internally in computers, enabling communication and processing. The section also introduces the concept of cipher, which is a coded form of data used to hide or encrypt information, which can later be decrypted to retrieve the original content. The importance of standard encoding schemes is emphasized, as they ensure that the code value assigned to a character (like 65 for 'A') is consistent across all keyboards and systems, regardless of their make or origin.

• Computers understand only binary language (0s and 1s).
• Each key on the keyboard is mapped to a unique code value internally.
• Encoding is the process of converting data into a coded form using specific codes.
• Example: 'A' is mapped to decimal 65, then converted to binary 1000001.
• Encoding ensures uniform representation of characters across devices.
• Cipher refers to data converted to a coded form for security (encryption).
• 📌 Encoding: The mechanism of converting data into an equivalent coded form using specific codes.
• 📌 Cipher: Data converted into coded form to hide or encrypt it.
• 📌 Binary Language: The language of computers using only digits 0 and 1.

2.1.1 American Standard Code for Information Interchange (ASCII)

This section explains the ASCII encoding scheme, developed in the early 1960s to standardize character representation across different computers. Before ASCII, computers had different ways of representing keyboard keys, which made communication between computers difficult. ASCII was created as a common standard to overcome this issue. ASCII originally used 7 bits to represent characters, which means it can encode 2^7 = 128 different characters. These include English alphabets (both uppercase and lowercase), digits, punctuation marks, and control characters. Table 2.1 in the textbook lists some printable ASCII characters along with their decimal values, such as space (32), '@' (64), 'A' (65), 'a' (97), and so on. ASCII is still the most commonly used coding scheme for English language characters. However, ASCII is limited to encoding only the English language character set and cannot represent characters from other languages or scripts. The section also includes an example where the word 'DATA' is encoded using ASCII codes and then converted into 7-bit binary codes for computer understanding. For instance, 'D' has ASCII value 68, which is 1000100 in binary. This example illustrates how textual data is converted into binary form using ASCII encoding. **Table on page 2 (11×6)** | Character | Decimal Value | Character | Decimal Value | Character | Decimal Value | | --- | --- | --- | --- | --- | --- | | Space | 32 | @ | 64 | ` | 96 | | ! | 33 | A | 65 | a | 97 | | " | 34 | B | 66 | b | 98 | | # | 35 | C | 67 | c | 99 | | $ | 36 | D | 68 | d | 100 | | % | 37 | E | 69 | e | 101 | | & | 38 | F | 70 | f | 102 | | ‘ | 39 | G | 71 | g | 103 | | ( | 40 | H | 72 | h | 104 | | ) | 41 | I | 73 | i | 105 | **Table on page 3 (3×5)** | | D | A | T | A | | --- | --- | --- | --- | --- | | ASCII Code | 68 | 65 | 84 | 65 | | Binary Code | 1000100 | 1000001 | 1010100 | 1000001 | **Table on page 12 (4×4)** | Digit | 2 | 5 | 7 | | --- | --- | --- | --- | | Position Number | 2 | 1 | 0 | | Positional Value | 8^{2} | 8^{1} | 8^{0} | | Decimal Number | 2 × 8^{2} | 5 × 8^{1} | + 7 × 8^{0} = 128 + 40 + 7 = (175)_{10} | **Table on page 12 (4×4)** | Digit | 3 | A | 5 | | --- | --- | --- | --- | | Position Number | 2 | 1 | 0 | | Positional Value | 16^{2} | 16^{1} | 16^{0} | | Decimal Number | 3 × 16^{2} | 10 × 16^{1} | + 5 × 16^{0} = 768 + 160 + 5 = (933)_{10} | **Table on page 12 (4×5)** | Digit | 1 | 1 | 0 | 1 | | --- | --- | --- | --- | --- | | Position Number | 3 | 2 | 1 | 0 | | Positional Value | 2^{3} | 2^{2} | 2^{1} | 2^{0} | | Decimal Number | 1 × 2^{3} | + 1 × 2^{2} | + 0 × 2^{1} | + 1 × 2^{0} = 8 + 4 + 0 + 1 = (13)_{10} | **Table on page 14 (3×4)** | Hexadecimal digits | 2 | 3 | D | | --- | --- | --- | --- | | Write 4-bit binary value for each digit | 0010 | 0011 | 1101 | | Therefore, $(23D)_{16} = (001000111101)_2$ | | | | **Table on page 14 (2×3)** | 0.25 × 2 = 0.50 | ↓ | 0 | | --- | --- | --- | | 0.50 × 2 = 1.00 | | 1 | **Table on page 15 (8×2)** | Integer part | | | --- | --- | | 0.675 × 2 = 1.350 | 1 | | 0.350 × 2 = 0.700 | 0 | | 0.700 × 2 = 1.400 | 1 | | 0.400 × 2 = 0.800 | 0 | | 0.800 × 2 = 1.600 | 1 | | 0.600 × 2 = 1.200 | 1 | | 0.200 × 2 = 0.400 | 0 | **Table on page 15 (6×2)** | Integer part | | | --- | --- | | 0.675 × 8 = 5.400 | 5 | | 0.400 × 8 = 3.200 | 3 | | 0.200 × 8 = 1.600 | 1 | | 0.600 × 8 = 4.800 | 4 | | 0.800 × 8 = 6.400 | 6 | **Table on page 15 (3×2)** | Integer part | | | --- | --- | | 0.675 × 16 = 10.800 | A (Hexadecimal symbol for 10) | | 0.800 × 16 = 12.800 | C (Hexadecimal symbol for 12) | **Table on page 16 (6×11)** | Digit | 1 | 0 | 0 | 1 | 0 | 1 | . | 1 | 0 | 1 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Fractional Value | 2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} | | 2^{-1} | 2^{-2} | 2^{-3} | | Decimal Value | 1×2^{5} | +0×2^{4} | +0×2^{3} | +1×2^{2} | +0×2^{1} | +1×2^{0} | + | 1×2^{-1} | +0×2^{-2} | +1×2^{-3} | | | = 32 | + 0 | + 0 | + 4 | + 0 | + 1 | + | 0.5 | + 0 | + 0.125 | | | 37 | | | | | | | 0.625 | | | | | = 37 + 0.625 | | | | | | | | | |

• ASCII was developed in the early 1960s to standardize character representation.
• It uses 7 bits to represent characters, allowing 128 unique characters.
• ASCII includes English alphabets, digits, punctuation, and control characters.
• ASCII codes are consistent across all keyboards and systems.
• ASCII cannot represent characters from non-English languages.
• Example: 'DATA' encoded as ASCII codes and converted to binary.
• 📌 ASCII: American Standard Code for Information Interchange, a 7-bit character encoding scheme.
• 📌 7-bit code: A binary code of length 7 bits used to represent characters.