The string of digitsħ24.5 is interpreted to represent the quantity
The quantity that the number represents, it is necessary to multiply each digitīy an integer power of r and then form the sum of all weighted digits.Įxample, the decimal number system in everyday use employs the radix 10 Numbers are represented by a string of digit symbols. Step 2 − Combine all the resulting binary groups (of 4 digits each) into a single binary number.A number system of base, or radix, r is a system that uses distinct symbols for 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 − Convert each group of four binary digits to one hexadecimal symbol.Ĭalculating hexadecimal Equivalent − Stepīinary Number − 10101 2 = Hexadecimal Number − 15 16 Shortcut method - Hexadecimal to Binary Step 1 − Divide the binary digits into groups of four (starting from the right). Octal Number − 25 8 = Binary Number − 10101 2 Shortcut method - Binary to Hexadecimal Step 2 − Combine all the resulting binary groups (of 3 digits each) into a single binary number. 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 − Convert each group of three binary digits to one octal digit.īinary Number − 10101 2 = Octal Number − 25 8 Shortcut method - Octal to Binary Step 1 − Divide the binary digits into groups of three (starting from the right). Octal Number − 25 8 = Binary Number − 10101 2 Shortcut method - Binary to Octal
Octal Number − 25 8 = Decimal Number − 21 10 Step 2 − Convert Decimal to Binary Stepĭecimal Number − 21 10 = Binary Number − 10101 2 Step 2 − Convert the decimal number so obtained to the new base number.Ĭalculating Binary Equivalent − Step 1 − Convert to Decimal Step Step 1 − Convert the original number to a decimal number (base 10). The total is the equivalent value in decimal. Step 3 − Sum the products calculated in Step 2. Step 2 − Multiply the obtained column values (in Step 1) by the digits in the corresponding columns. 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). Example −Īs 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).ĭecimal Number − 29 10 = Binary Number − 11101 2. The last remainder thus obtained will be the Most Significant Digit (MSD) of the new base number.
Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3. Step 4 − Record the remainder from Step 3 as the next digit (to the left) of the new base number. Step 3 − Divide the quotient of the previous divide by the new base. Step 2 − Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number. Step 1 − Divide the decimal number to be converted by the value of the new base. Shortcut method − Hexadecimal to Binary.Shortcut method − Binary to Hexadecimal.There are many methods or techniques which can be used to convert numbers from one base to another.