<h5 id="21-introduction">2.1 INTRODUCTION</h5> <ul> <li>The process of converting data into an equivalent coded form using specific codes is called encoding.</li> <li>When a key on the keyboard is pressed, it is internally mapped to a unique decimal, hexadecimal or binary value, which is further converted to binary for the computer to understand.</li> <li>For example, the key ‘A’ is mapped to a decimal value 65 and hexadecimal 0905, whose binary equivalent is 01000001 and 00001001 00000101 respectively.</li> <li>This encoding is standardized, meaning each letter, numeral, and symbol is encoded with a unique code, which is the same for all keyboards.</li> <li>Some well-known encoding schemes include these standardized codes.</li> </ul> <p>======</p> <h5 id="211-american-standard-code-for-information-interchange-ascii">2.1.1 American Standard Code for Information Interchange (ASCII)</h5> <ul> <li>In the given text, ASCII values of certain characters are provided.</li> <li>ASCII value of Space is 32.</li> <li>ASCII value of " (double quote) is 34.</li> <li>ASCII value of ! (exclamation mark) is 33.</li> <li>ASCII values of a (lowercase and uppercase) are 97 and 65 respectively.</li> <li>ASCII values of b (lowercase and uppercase) are 98 and 66 respectively.</li> <li>The ASCII value of - (hyphen or minus) is 45, but it is given as 96$. This could be an error.</li> </ul> <p>======</p> <h5 id="-35--c--67--c--99">| 35 | C | 67 | c | 99</h5> <ul> <li>ASCII and Binary codes are numerical representations for characters. For ASCII, each character is assigned a unique number from 0 to 127. In the given example, 68 represents ‘D’, 65 represents ‘A’, 84 represents ‘T’, and so on.</li> <li>UNICODE is a standard that assigns every character, from any language, a unique identifier. This includes characters from Indian languages.</li> <li>To type in an Indian language using UNICODE, no additional tool or font needs to be installed, as long as the application or operating system supports UNICODE.</li> <li>However, the user may need to enable the use of UNICODE characters or the specific Indian language in the application or operating system.</li> <li>It’s important to note that while UNICODE provides the identifiers, the visual representation of the characters (i.e., the font) must also support the specific Indian language.</li> </ul> <p>======</p> <h5 id="212-indian-script-code-for-information-interchange-iscii">2.1.2 Indian Script Code for Information Interchange (ISCII)</h5> <ul> <li>ISCII (Indian Script Code for Information Interchange) is an 8-bit code representation for Indian languages, developed in the mid-1980s.</li> <li>It retains all 128 ASCII codes and uses the rest of the codes (128) for additional Indian language character sets.</li> <li>The additional codes have been assigned in the upper region (160-255) for the ‘aksharas’ (characters) of the language.</li> <li>ISCII is not used for typing in UNICODE, however, UNICODE is a widely used standard for encoding, representing, and handling text expressed in most of the world’s writing systems.</li> <li>For typing in Indian languages in UNICODE, you can explore and list down font names such as: <ul> <li>For Hindi: “Lohit Hindi” and “Arial Unicode MS”</li> <li>For Bengali: “Lohit Bengali” and “Arial Unicode MS”</li> <li>For Tamil: “Lohit Tamil” and “Arial Unicode MS”</li> </ul> </li> </ul> <p>Note: The above list of font names is for illustrative purposes only, and there might be other fonts available as well.</p> <p>======</p> <h5 id="213-unicode">2.1.3 Unicode</h5> <ul> <li>The UNICODE standard was developed to incorporate all the characters of every written language, providing a unique number for every character.</li> <li>It is a superset of ASCII, and the values $0-128$ have the same character as in ASCII.</li> <li>Commonly used UNICODE encodings are UTF-8, UTF-16, and UTF-32.</li> <li>The space required for a character in UTF-32 is more than in UTF-16 or UTF-8.</li> <li>UNICODE characters for Devanagari script are shown in Table 2.3, with each cell containing a character along with its equivalent hexadecimal value.</li> </ul> <p>======</p> <h5 id="22-number-system">2.2 NUMBER SYSTEM</h5> <ul> <li>The text introduces the positional notation system used in mathematics, specifically in base 10.</li> <li>Each digit in a number has a positional value, which is calculated as $(10)^n$, where $n$ is the position of the digit from right to left, starting from 0.</li> <li>The decimal number is obtained by adding the product of each digit and its positional value.</li> <li>For example, the decimal number $(123.45)_{10}$ can be computed using the positional values of its digits.</li> <li>Figure 2.3 in the text illustrates the computation of decimal numbers using their positional values.</li> </ul> <p>======</p> <h5 id="221-decimal-number-system">2.2.1 Decimal Number System</h5> <ul> <li>The decimal number system is a base-1</li> </ul> <p>======</p> <h5 id="222-binary-number-system">2.2.2 Binary Number System</h5> <ul> <li>The text discusses the concept of significant figures in measurement.</li> <li>Significant figures are important in expressing the precision of a measurement.</li> <li>The rules for counting significant figures in a number are: all non-zero digits are significant, and zeroes are significant if they are between non-zero digits.</li> <li>In a number with a decimal point, trailing zeros after the decimal point are significant.</li> <li>When multiplying or dividing measurements, the number of significant figures in the result is determined by the measurement with the fewest significant figures.</li> <li>When adding or subtracting measurements, the result should be rounded to the same number of decimal places as the measurement with the fewest decimal places.</li> </ul> <p>======</p> <h5 id="223-octal-number-system">2.2.3 Octal Number System</h5> <ul> <li>The text presents a summary of binary numeral system.</li> <li>In binary, there are only two possible digits: 0 and 1.</li> <li>Binary numbers are created by concatenating 0s and 1s, similar to how decimal numbers are created using 0-9.</li> <li>The position of a digit in a binary number determines its weight or value, with the rightmost digit being the least significant and the leftmost digit being the most significant.</li> <li>The binary system is used in digital electronics and is the foundation for computer processing and storage.</li> </ul> <p>======</p> <h5 id="224-hexadecimal-number-system">2.2.4 Hexadecimal Number System</h5> <ul> <li>The text presents a binary-to-decimal conversion table.</li> <li>The binary numbers range from 0 to 14, represented as 4-bit binary digits (0000 to 1111).</li> <li>The decimal equivalents range from 0 to 15.</li> <li>There is a direct correspondence between binary and decimal numbers in the table.</li> <li>The decimal equivalent of a binary number is found by adding the decimal equivalents of each binary digit, where the rightmost digit has a weight of 1, the second digit from the right has a weight of 2, and so on.</li> </ul> <p>======</p> <h5 id="225-applications-of-hexadecimal-number-system">2.2.5 Applications of Hexadecimal Number System</h5> <ul> <li>In the given text, different colors are represented in various numerical formats.</li> <li>The color Black is represented as $(0,0,0)$, $(00000000,00000000,00000000)$, or $(00,00,00)$.</li> <li>The color White is represented as $(255,255,255)$, $(11111111,11111111,11111111)$, or $(\text{FF}, \text{FF}, \text{FF})$.</li> <li>The color Yellow is represented as $(255,255,0)$, $(1111111,11111111,00000000)$, or $(\text{FF}, \text{FF}, 00)$.</li> <li>The color Grey is represented as $(128,128,128)$, $(10000000,10000000,10000000)$, or $(80,80,80)$.</li> </ul> <p>======</p> <h5 id="23-conversion-between-number-systems">2.3 CONVERSION BETWEEN NUMBER SYSTEMS</h5> <ul> <li>The process of converting numbers from one number system to another is important for better understanding of number representation in computers.</li> <li>Decimal number system is commonly used by humans, while digital systems understand binary numbers.</li> <li>Octal and hexadecimal number systems are used to simplify the binary representation for humans to understand.</li> <li>Activity 2.2 involves converting decimal numbers to the form understood by computers: <ol> <li>$(593)<em>{10}$ in binary is $(1000101001)</em>{2}$</li> <li>$(326)<em>{10}$ in binary is $(101000110)</em>{2}$</li> <li>$(79)<em>{10}$ in binary is $(1001111)</em>{2}$</li> </ol> </li> <li>Binary representation can be further converted to octal or hexadecimal number systems for easier understanding.</li> </ul> <p>======</p> <h5 id="231-conversion-from-decimal-to-other-number-systems">2.3.1 Conversion from Decimal to other Number Systems</h5> <ul> <li>The given text outlines the process to convert decimal numbers to other number systems, including binary, octal, and hexadecimal.</li> <li>To convert decimal to binary: Divide the decimal number by 2 and note the remainder till the quotient is 0, then write the remainders in reverse order.</li> <li>To convert decimal to octal: Divide the decimal number by 8 and note the remainder till the quotient is 0, then write the remainders in reverse order.</li> <li>To convert decimal to hexadecimal: Divide the decimal number by 16 and note the remainder till the quotient is 0, then write the remainders in reverse order.</li> <li>Examples of decimal to octal conversions: (913)10 to (1711)8, (845)10 to (1455)8, and (66)10 to (102)8.</li> <li>Examples of decimal to binary and hexadecimal conversions are also provided in the text.</li> </ul> <p>======</p> <h5 id="232-conversion-from-other-number-systems-to-decimal-number-system">2.3.2 Conversion from other Number Systems to Decimal Number System</h5> <ul> <li> <p>The process of converting numbers from other number systems to decimal number system involves writing the position number for each symbol, getting positional value for each symbol by raising its position number to the base value, multiplying each digit with the respective positional value to get a decimal value, and adding all these decimal values to get the equivalent decimal number.</p> </li> <li> <p>To convert binary numbers to decimal, positional values are computed in terms of powers of 2. For example, to convert $(1101)_{2}$ into decimal, the positional values would be $2^3$, $2^2$, $2^1$, and $2^0$, and the decimal equivalent would be $1<em>2^5 + 1</em>2^3 + 0<em>2^2 + 1</em>2^1 + 1*2^0 = 56+8+0+2+1 = 67$.</p> </li> <li> <p>To convert octal numbers to decimal, positional values are computed in terms of powers of 8. For example, to convert $(257)_{8}$ into decimal, the positional values would be $8^2$ and $8^0$, and the decimal equivalent would be $2<em>8^2 + 5</em>8^1 + 7*8^0 = 208+40+7 = 255$.</p> </li> <li> <p>The base value of octal number system is 8, which is equivalent to $2^3$. Therefore, three binary digits are sufficient to represent all 8 octal digits.</p> </li> <li> <p>To convert hexadecimal numbers to decimal, positional values are computed in terms of powers of 16. The decimal equivalent of alphabet symbols in hexadecimal numbers can be found in Table 2.6. For example, to convert $(COF5)_{16}$ into decimal, the positional values would be $16^3$, $16^2$, $16^1$, and $16^0$, and the decimal equivalent would be $12<em>16^3 + 15</em>16^2 + 15<em>16^1 + 5</em>16^0 = 491520 + 38400 + 3840 + 5 = 531765$.</p> </li> </ul> <p>======</p> <h5 id="233-conversion-from-binary-number-to-octal-hexadecimal-number-and">2.3.3 Conversion from Binary Number to Octal/ Hexadecimal Number and</h5> <ul> <li>Binary numbers can be converted to octal by grouping 3 bits together from right to left and replacing each group with its equivalent octal digit. If the number of bits is not a multiple of 3, add 0s on the most significant position.</li> <li>Octal numbers can be converted to binary by replacing each octal digit with its equivalent 3-bit binary number.</li> <li>Binary numbers can be converted to hexadecimal by grouping 4 binary digits together from right to left and substituting each 4-bit group with its equivalent hexadecimal alphanumeric symbol.</li> <li>Hexadecimal numbers can be converted to binary by substituting the 4-bit binary equivalent of each hexadecimal digit and combining them together.</li> <li>The binary representation of (F018)16 is 1111000000011000, (172)16 is 000101110010, and (613)8 is 01100001001.</li> </ul> <p>======</p> <h5 id="234-conversion-of-a-number-with-fractional-part">2.3.4 Conversion of a Number with Fractional Part</h5> <ul> <li>To convert the fractional part of a decimal number to another number system with base value $b$, repeatedly multiply the fractional part by the base value $b$ till the fractional part becomes</li> </ul> <p>======</p>