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write as you are wring a proper solution in exam paper with proper steps , and correct " Consider a decimal number 96. Find out the equivalent representation and number of digits needed to represent the decimal number in binary, octal, and hexadecimal representations suitable for modern computers. For example, representing the decimal number 13 requires 5 digits in binary (01101), two digits in octal (15), and two digits in hexadecimal (0D).

Sure, let's perform the conversions for the decimal number 96 to binary, octal, and hexadecimal number systems.

  1. Conversion from Decimal to Binary:

Step 1: Divide the decimal 96 by 2 and record the remainder.

    96 / 2 = 48 remainder 0

Step 2: Continue the process of division by 2 with the quotient obtained in the previous step.

    48 / 2 = 24 remainder 0
    24 / 2 = 12 remainder 0
    12 / 2 = 6  remainder 0
    6 /  2 = 3  remainder 0
    3 /  2 = 1  remainder 1
    1 /  2 = 0  remainder 1

Step 3: The binary representation is obtained by arranging the remainders bottom-to-top.

     Thus, 96 (decimal) = 1100000 (binary).

The binary representation of decimal 96 requires 7 digits.

  1. Conversion from Decimal to Octal:

Step 1: Divide the decimal number 96 by 8 and record the remainder.

    96 / 8 = 12 remainder 0

Step 2: Continue the process of division by 8 with the quotient obtained in the previous step.

    12 / 8 = 1 remainder 4
    1 /  8 = 0 remainder 1

Step3: The octal representation is by arranging the remainders bottom-to-top.

     Thus, 96 (decimal) = 140 (octal).

The octal representation of decimal 96 requires 3 digits.

  1. Conversion from Decimal to Hexadecimal:

Step 1: Divide the decimal number 96 16 and record the.

    96 / 16 = 6  remainder 0

Step 2: Continue the process of division by 16 with the quotient obtained in the previous step until it eventually becomes 0. In this case, the next step results in 0.

    6 /  16 = 0  remainder 6

Step 3: The hexadecimal values for decimal numbers range from 0 to 9 and A to F for 10 to 15. The hexadecimal representation is obtained by arranging the remainders bottom-to-top.

    Thus, 96 (decimal) = 60 (hexadecimal).

The hexadecimal representation of decimal 96 requires 2 digits.

To conclude, we can the decimal number 96 using 7 digits in binary (1100000), 3 digits in octal (140), and 2 digits in hexadecimal (60).

Depending on its purpose, computer programming uses different numbering systems. Explore number systems, and learn about converting between binary, decimal, octal, and hexadecimal numbers. Updated: 08/02/2023 Number Systems Conversions: Decimal to Others Conversions: Binary to Others Conversions: Octal to Others Conversions: Hexadecimal to Others Lesson Summary The number system that most of us are familiar with is known as the decimal system, which is based on base 10 and the place values are based on the powers of 10. From right to left, we have the ones place, the tens place, the hundreds place, the thousands place, and so on. Each digit can have the value zero, one, two, three, and so on through nine. The number 768 represents seven hundreds, six tens, and eight ones, giving us the value we recognize as 'seven hundred and sixty-eight.' To unlock this lesson you must be a Study.com Member. Create your account Video Quiz Course To convert from decimal to other number systems, we use a repeated process of division and dividing remainders. We begin by taking the largest power of our new base and dividing our original number by the new base. The quotient gives us our digit, and the process is repeated on the remainder. This process has to be repeated until we divide by the final 1 to get the last digit. Let's convert the number 35 from decimal to binary, octal, and hexadecimal. In converting to binary, we need to know the powers of 2, which are 1, 2, 4, 8, 16, 32, 64, and so on. We'll start with 32 since 32 is smaller than our initial number of 35, and 64 is larger. To unlock this lesson you must be a Study.com Member. Create your account To convert from binary to decimal, we use a process of multiplication and addition. To convert the binary number 0110 1010 to decimal, we take each digit, from right to left, multiply it by the place value, and add it to our running total. 0 1 = 0, add 0 1 2 = 2, add 2, get 2 0 4 = 0, add 0, get 2 1 8 = 8, add 8, get 10 0 16 = 0, add 0, get 10 1 32 = 32, add 32, get 42 1 64 = 64, add 64, get 106 0 128 = 0, add 0, get 106. The answer is that 0110 1010 binary = 106 decimal. To unlock this lesson you must be a Study.com Member. Create your account To convert from octal to decimal, we use a process of multiplication and addition. To convert the octal number 123 to decimal, we take each digit, from right to left, multiply it by the place value, and add it to our running total. 3 1 = 3, add 3 2 8 = 16, add 16, get 19 1 64 = 64, add 64, get 83. The answer then is 123 octal = 83 decimal. To convert from octal to binary, we can take a shortcut. Because each octal digit represents 3 bits, we simply expand each octal digit into the 3 bits it represents. This process can be done from left to right. To unlock this lesson you must be a Study.com Member. Create your account To convert from hexadecimal to decimal, we use a process of multiplication and addition. Hexadecimal numbers can represent a larger number in a smaller space, so we'll use a small number as an example. The same principles for conversion apply even for larger numbers. To convert the hexadecimal number 2F to decimal, we take each digit, from right to left, multiply it by the place value, and add it to our running total. F 1 = 15, add 15 2 16 = 32, add 32, get 47. The answer then is 2F hexadecimal = 47 decimal. To unlock this lesson you must be a Study.com Member. Create your account Let's review the number systems: Decimal system: based on base 10 and the place values are based on the powers of 10. Binary system: where there are only two possible values for each digit, zero or one. Octal system: the value of each place is based on the powers of 8. Hexadecimal system: the value of each place is based on the powers of 16. Here's a recap of conversions: To unlock this lesson you must be a Study.com Member. Create your account Register to view this lesson Are you a student or a teacher? Unlock Your Education See for yourself why 3

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Decimal to Binary, Hex & Octal Conversion - work with stepsHomeMathPre-AlgebraInput Data :Decimal = 24Objective :Find what is binary, hex & octal Value from decimal number?Solution :Decimal to Binary2242120260230211201Write the Ramainders from bottom to top`24_10 = 11000_2`Decimal to Hexa DecimalWrite the Ramainders from bottom to top`24_10 = 18_16`Decimal to OctalWrite the Ramainders from bottom to top`24_10 = 30_8`Decimal to Binary, Hex & Octal Converter to perform decimal to binary, decimal to hex & decimal to octal conversion online by using simple successive division methods along with step by step calculation & solved example problems. Decimal conversions can be done by either successive division method or successive multiplication method. The example problems have been accomplished by using successive division method to find the equivalent numbers in binary, hex & octal number systems.Decimal to Binary ConversionThe below solved example along with step by step calculation for decimal to binary conversion let the users to understand how to perform such conversion manually.Step by step conversion:step 1: For decimal to binary conversion by successive division, divide the decimal number by 2 until the quotient reach to 1 or 0.step 2: Note down every remainder (normally 1 or 0) for each successive division by 2. The first & last remainder is the LSD (least significant digit or bit) & MSD (most significant digit or bit) respectively.step 3: Arranging the remainder from MSD to LSD is the equivalent binary for the given decimal.Solved Example:Convert the decimal number 37 to its binary equivalentDecimal to Hex ConverterThe below solved example along with step by step calculation for decimal to hexa-decimal conversion let the users to understand how to perform such conversions manually.Step by step conversion:step 1: For decimal to hex conversion by successive division, divide the decimal number by 16 until the quotient reach to 0 or less than 16.step 2: Note down every remainder (normally decimal numbers less than or equals to 15) for each successive division by 16. The first & last remainder is the LSD (least significant digit or bit) & MSD (most significant digit or bit) respectively.step 3: Arranging the remainder from MSD to LSD is the equivalent hex number for the given decimal.Solved Example:Convert Decimal number 3509 to its Hex equivalentDecimal to Octal Converterhe below solved example along with step by step calculation for decimal to octal conversion let the users to understand how to perform such conversions manually.Step by step conversion:step 1: For decimal to octal conversion by successive division, divide the decimal number by 8 until the quotient reach to 0 or less than 8.step 2: Note down every remainder (normally decimal numbers less than or equals to 7) for each successive division by 8 (normally decimal numbers less than or equals to 7). The first & last remainder is the LSD (least significant digit or bit) & MSD (most significant digit or bit) respectively.step 3: Arranging the remainder from MSD to LSD is the equivalent octal number for the given decimal.Solved Example:Convert the decimal number 214 to its octal equivalentThe number conversion is being used in various general & digital applications, therefore, sometimes it's important to perform the conversion between different digital number systems. The step by step calculation & solved examples may useful for users to understand how the values are being used in the examples, however, when it comes to online for quick calculations, this Decimal to Binary, Hex & Octal Converter helps the user to perform & verify such calculations as quick & easy as possible.Prime or Composite Number CalculatorPrime Factorization CalculatorArithmetic Progression CalculatorGeometric Progression CalculatorBillion - Million - Crores - Lakhs ConverterBinary to Decimal, Hex & Octal ConverterHex to Decimal, Binary & Octal ConverterOctal to Decimal, Binary & Hex ConverterWeigh

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To convert decimal to octal, we have to learn about both the number systems first. A number with base 8 is the octal number and a number with base 10 is the decimal number. Here we will convert a decimal number to an equivalent octal number. It is the same as converting any decimal number to binary or decimal to hexadecimal. In decimal to binary, we divide the number by 2, in decimal to hexadecimal we divide the number by 16. In case of decimal to octal, we divide the number by 8 and write the remainders in the reverse order to get the equivalent octal number. Decimal Number: All the numbers to the base ten are called decimal numbers. These are the commonly used numbers, which are 0-9. It has both integer part and the decimal part. It is separated by a decimal point (.). Numbers on the left of the decimal are integers and numbers on the right of the decimal is the decimal part. Example: (236.89)10, (54.2)10, etc. Octal number: These are the numbers with base 8. If x is a number then the octal number is denoted as x8. It contains digits from 0 to 7. Example: (212)8, (121)8, etc. Convert Decimal to Octal with Steps Follow the steps given below to learn the decimal to octal conversion: Write the given decimal number If the given decimal number is less than 8 the octal number is the same. If the decimal number is greater than 7 then divide the number by 8. Note the remainder, we get after division Repeat step 3 and 4 with the quotient till it is less than 8 Now, write the remainders in reverse order (bottom to top) The resultant is the equivalent octal number to the given decimal number. For example: Convert 1792 into an octal number. Decimal Number Operation Quotient Remainder Octal Number 1792 8 224 0 0 224 8 28 0 00 28 8 3 4 400 3 8 0 3 3400 Also, read: Decimal Fractions Octal Number System Important Questions Class 9 Maths Chapter 1 Number System Decimal to Octal Table Decimal Equivalent Octal Number Decimal Equivalent Octal Number 0 0 9 11 1 1 10 12 2 2 11 13 3 3 12 14 4 4 13 15 5 5 14 16 6 6 15 17 7 7 16 20 8 10 17 21 Solved Examples Example 1: Convert (127)10 to Octal. Solution: Divide 127 by 8 127 8= 15(Quotient) and (7)Remainder Divide 15 by 8 again. 15 8 = 1(Quotient) and (7) Remainder Divide 1 by 8, we get; 1 8 = 0(Quotient) and (1) Remainder Since the quotient is zero now, no more division can be done. So by taking the remainders in reverse order, we get the equivalent octal number. Hence, (127)10 = (177)8 Example 2: Convert 5210 to octal. Solution: Divide 52 by 8 52 8 = 6(Quotient) and (4)Remainder Divide 6 by 8 again. 6 8 = 0(Quotient) and (6) Remainder Since the quotient is zero now, no more division can be done. So by taking the remainders in reverse order, we get the equivalent octal number. Hence, (52)10 = (64)8 Example 3: Convert 10010 to octal. Solution: Divide 100 by 8 100 8= 12(Quotient) and (4)Remainder Divide 12 by 8 again. 12 8 = 1(Quotient) and (4) Remainder Divide 1 by 8, we get; 1 8 = 0(Quotient) and (1) Remainder Since the quotient is zero now, no more division can be done. So by taking the remainders in reverse order, we get the equivalent octal number. Hence, (100)10 = (144)8 Practice Questions Convert 45610 to Octal (Answer: 7108) Convert 21210 to Octal (Answer: 3248) Convert 10110to Octal (Answer: 1458)

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