Decimal to Binary
Binary Number System:
Conversion of Decimal number to Binary number:
Set up the problem. For this example, let's convert the decimal number 15610 to binary.
Write the decimal number as the dividend inside an upside-down "long division" symbol.
Write the base of the destination system (in our case, "2" for binary) as the divisor outside the curve of the division symbol.
Write the integer answer (quotient) under the long division symbol, and write the remainder (0 or 1) to the right of the dividend. Basically, if the dividend is even, the binary remainder will be 0; if the dividend is odd, the binary remainder will be 1.
Continue downwards, dividing each new quotient by two and writing the remainders to the right of each dividend. Stop when the quotient is 0.
Starting with the bottom remainder, read the sequence of remainders upwards to the top. For this example, you should have 10011100. This is the binary equivalent of the decimal number 156. Or, written with base subscripts: 15610 = 100111002
This method can be modified to convert from decimal to any base. The divisor is 2 because the desired destination is base 2. If the desired destination is a different base, replace the 2 in the method with the desired base. For example, if the desired destination is base 8 or 16 (ie.octal or hexa decimal), replace the 2 with 8 or 16. The final result will then be in the desired base.
Conversion of Binary number to Decimal number:
For this example, let's convert the binary number 100110112 to decimal. List the powers of two from right to left. Start at 20, evaluating it as "1". Increment the exponent by one for each power. Stop when the amount of elements in the list is equal to the amount of digits in the binary number. The example number, 10011011, has eight digits, so the list, to eight elements, would look like this: 128, 64, 32, 16, 8, 4, 2, 1
Write first the binary number below the list.
Draw lines, starting from the right, connecting
Conversion of Decimal number to Binary number:
Set up the problem. For this example, let's convert the decimal number 15610 to binary.
Write the decimal number as the dividend inside an upside-down "long division" symbol.
Write the base of the destination system (in our case, "2" for binary) as the divisor outside the curve of the division symbol.
Write the integer answer (quotient) under the long division symbol, and write the remainder (0 or 1) to the right of the dividend. Basically, if the dividend is even, the binary remainder will be 0; if the dividend is odd, the binary remainder will be 1.
Continue downwards, dividing each new quotient by two and writing the remainders to the right of each dividend. Stop when the quotient is 0.
Starting with the bottom remainder, read the sequence of remainders upwards to the top. For this example, you should have 10011100. This is the binary equivalent of the decimal number 156. Or, written with base subscripts: 15610 = 100111002
This method can be modified to convert from decimal to any base. The divisor is 2 because the desired destination is base 2. If the desired destination is a different base, replace the 2 in the method with the desired base. For example, if the desired destination is base 8 or 16 (ie.octal or hexa decimal), replace the 2 with 8 or 16. The final result will then be in the desired base.
Conversion of Binary number to Decimal number:
For this example, let's convert the binary number 100110112 to decimal. List the powers of two from right to left. Start at 20, evaluating it as "1". Increment the exponent by one for each power. Stop when the amount of elements in the list is equal to the amount of digits in the binary number. The example number, 10011011, has eight digits, so the list, to eight elements, would look like this: 128, 64, 32, 16, 8, 4, 2, 1
Write first the binary number below the list.
Draw lines, starting from the right, connecting