how many number system conversion ? write their base number
Answers
Answer:
ohk
Step-by-step explanation:
tThere are many methods or techniques which can be used to convert numbers from one base to another. We'll demonstrate here the following −
Decimal to Other Base System
Other Base System to Decimal
Other Base System to Non-Decimal
Shortcut method − Binary to Octal
Shortcut method − Octal to Binary
Shortcut method − Binary to Hexadecimal
Shortcut method − Hexadecimal to Binary
Decimal to Other Base System
Steps
Step 1 − Divide the decimal number to be converted by the value of the new base.
Step 2 − Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number.
Step 3 − Divide the quotient of the previous divide by the new base.
Step 4 − Record the remainder from Step 3 as the next digit (to the left) of the new base number.
Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3.
The last remainder thus obtained will be the Most Significant Digit (MSD) of the new base number.
Example −
Decimal Number: 2910
Calculating Binary Equivalent −
StepOperationResultRemainderStep 129 / 2141Step 214 / 270Step 37 / 231Step 43 / 211Step 51 / 201
As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the first remainder becomes the Least Significant Digit (LSD) and the last remainder becomes the Most Significant Digit (MSD).
Decimal Number − 2910 = Binary Number − 111012.
Other Base System to Decimal System
Steps
Step 1 − Determine the column (positional) value of each digit (this depends on the position of the digit and the base of the number system).
Step 2 − Multiply the obtained column values (in Step 1) by the digits in the corresponding columns.
Step 3 − Sum the products calculated in Step 2. The total is the equivalent value in decimal.
Example
Binary Number − 111012
Calculating Decimal Equivalent −
StepBinary NumberDecimal NumberStep 1111012((1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20))10Step 2111012(16 + 8 + 4 + 0 + 1)10Step 31110122910
Binary Number − 111012 = Decimal Number − 2910
Other Base System to Non-Decimal System
Steps
Step 1 − Convert the original number to a decimal number (base 10).
Step 2 − Convert the decimal number so obtained to the new base number.
Example
Octal Number − 258
Calculating Binary Equivalent −
Step 1 − Convert to Decimal
StepOctal NumberDecimal NumberStep 1258((2 × 81) + (5 × 80))10Step 2258(16 + 5 )10Step 32582110
Octal Number − 258 = Decimal Number − 2110
Step 2 − Convert Decimal to Binary
StepOperationResultRemainderStep 121 / 2101Step 210 / 250Step 35 / 221Step 42 / 210Step 51 / 201
Decimal Number − 2110 = Binary Number − 101012
Octal Number − 258 = Binary Number − 101012
Shortcut method - Binary to Octal
Steps
Step 1 − Divide the binary digits into groups of three (starting from the right).
Step 2 − Convert each group of three binary digits to one octal digit.
Example
Binary Number − 101012
Calculating Octal Equivalent −
StepBinary NumberOctal NumberStep 1101012010 101Step 210101228 58Step 3101012258
Binary Number − 101012 = Octal Number − 258
Shortcut method - Octal to Binary
Steps
Step 1 − Convert each octal digit to a 3 digit binary number (the octal digits may be treated as decimal for this conversion).
Step 2 − Combine all the resulting binary groups (of 3 digits each) into a single binary number.
Example
Octal Number − 258
Calculating Binary Equivalent −
StepOctal NumberBinary NumberStep 1258210 510Step 22580102 1012Step 32580101012
Octal Number − 258 = Binary Number − 101012
Shortcut method - Binary to Hexadecimal
Steps
Step 1 − Divide the binary digits into groups of four (starting from the right).
Step 2 − Convert each group of four binary digits to one hexadecimal symbol.
Example
Binary Number − 101012
Calculating hexadecimal Equivalent −
StepBinary NumberHexadecimal NumberStep 11010120001 0101Step 2101012110 510Step 31010121516
Binary Number − 101012 = Hexadecimal Number − 1516
Shortcut method - Hexadecimal to Binary
Steps
Step 1 − Convert each hexadecimal digit to a 4 digit binary number (the hexadecimal digits may be treated as decimal for this conversion).
Step 2 − Combine all the resulting binary groups (of 4 digits each) into a single binary number.
Example
Hexadecimal Number − 1516
Calculating Binary Equivalent −
StepHexadecimal NumberBinary NumberStep 11516110 510Step 2151600012 01012Step 31516000101012
Hexadecimal Number − 1516 = Binary Number − 101012
Answer:
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