Download ICT - Lecture - Number System Conversion and more Lecture notes Information and Communications Technology (ICT) in PDF only on Docsity!
NNUUMMBBEERR SSYYSSTTEEMM CCOONNVVEERRSSIIOONN
There 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 leastsignificantdigit 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 totheleft of the new base number. Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step
The last remainder thus obtained will be the Most Significant Digit MSD of the new base number.
Example −
Decimal Number: 29 10 Calculating Binary Equivalent − Step Operation Result Remainder Step 1 29 / 2 14 1 Step 2 14 / 2 7 0 Step 3 7 / 2 3 1 Step 4 3 / 2 1 1 Step 5 1 / 2 0 1 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 thisdependsonthepositionofthedigitandthebaseofthenumbersystem. Step 2 − Multiply the obtained column values inStep 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 − 11101 2 Calculating Decimal Equivalent − Step Binary Number Decimal Number Step (^1 111012) ((1 × 24 ) + (1 × 23 ) + (1 × 22 ) + (0 × 21 ) + (1 × 20 )) 10 Step 2 (^111012 16) + 8 + 4 + 0 + (^1 ) Step (^3 111012 ) Binary Number − 11101 2 = Decimal Number − 29 10
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
Step Octal Number Decimal Number Step (^1 258) ((2 × 8^1 ) + (5 × 8^0 )) 10 Step (^2 258 16) + (^5 ) Step (^3 258 ) Octal Number − 258 = Decimal Number − (^2110)
Step 2 − Convert Decimal to Binary
16 Loading [MathJax]/jax/output/HTML-CSS/jax.js Step (^3 258 ) Octal Number − 25 8 = Binary Number − 10101 2
Shortcut method - Binary to Hexadecimal
Steps Step 1 − Divide the binary digits into groups of four startingfromtheright. Step 2 − Convert each group of four binary digits to one hexadecimal symbol.
Example
Binary Number − (^101012) Calculating hexadecimal Equivalent − Step Binary Number Hexadecimal Number Step 1 101012 0001 0101 Step (^2 101012 110 ) Step (^3 101012 ) Binary Number − 101012 = Hexadecimal Number − (^1516)
Shortcut method - Hexadecimal to Binary
Steps Step 1 − Convert each hexadecimal digit to a 4 digit binary number thehexadecimaldigitsmaybetreatedasdecimalforthisconversion. Step 2 − Combine all the resulting binary groups of 4 digitseach into a single binary number.
Example
Hexadecimal Number − (^1516) Calculating Binary Equivalent − Step Hexadecimal Number Binary Number Step (^1 1516 110 ) Step (^2 1516 00012 ) Step (^3 1516 ) Hexadecimal Number − 15 = Binary Number – (^101012)
BINARY ARITHMETIC
OCTAL ARITHMETIC
