Question
Perform the following conversion of numbers:
i) Decimal (3456345123)10 to binary and hexadecimal
ii) Hexadecimal (CABFF114)h into Octal.
Answer :
Word Count : 1314
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Skip in 10
The conversion of number systems is an important operation in Computer Organization and Assembly Language Programming because computers internally represent and process data in binary form, while hexadecimal and octal systems provide compact ways of representing binary values. Decimal numbers use ten digits, from 0 to 9, whereas binary uses only 0 and 1, hexadecimal uses sixteen symbols from 0 to 9 and A to F, and octal uses eight digits from 0 to 7. The given conversions can be performed systematically by repeated division and by grouping binary digits. For the first conversion, the given decimal number is (3456345123)₁₀ To convert a decimal integer into binary, the number is repeatedly divided by 2. At every division, the remainder is either 0 or 1. The quotient is again divided by 2 until the quotient becomes zero. The binary number is obtained by reading the remainders from bottom to top. The repeated division process is: 3456345123 ÷ 2 = 1728172561 remainder 1 1728172561 ÷ 2 = 864086280 remainder 1 864086280 ÷ 2 = 432043140 remainder 0 432043140 ÷ 2 = 216021570 remainder 0 216021570 ÷ 2 = 108010785 remainder 0 108010785 ÷ 2 = 54005392 remainder 1 54005392 ÷ 2 = 27002696 remainder 0 27002696 ÷ 2 = 13501348 remainder 0 13501348 ÷ 2 = 6750674 remainder 0 6750674 ÷ 2 = 3375337 remainder 0 3375337 ÷ 2 = 1687668 remainder 1 1687668 ÷ 2 = 843834 remainder 0 843834 ÷ 2 = 421917 remainder 0 421917 ÷ 2 = 210958 remainder 1 210958 ÷ 2 = 105479 remainder 0 105479 ÷ 2 = 52739 remainder 1 52739 ÷ 2 = 26369 remainder 1 26369 ÷ 2 = 13184 remainder 1 13184 ÷ 2 = 6592 remainder 0 6592 ÷ 2 = 3296 remainder 0 3296 ÷ 2 = 1648 remainder 0 1648 ÷ 2 = 824 remainder 0 824 ÷ 2 = 412 remainder 0 412 ÷ 2 = 206 remainder 0 206 ÷ 2 = 103 remainder 0 103 ÷ 2 = 51 remainder 1 51 ÷ 2 = 25 remainder 1 25 ÷ 2 = 12 remainder 1 12 ÷ 2 = 6 remainder 0 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Reading these remainders from the last division to the first gives: (3456345123)₁₀ = (11001110000000111010010000100011)₂ Thus, the required binary representation is: (11001110000000111010010000100011)₂ The same decimal number can be converted into
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