Saturday, 6 April 2013

Easy ways to convert Binary into Decimal

As we know that binary numbers are numbers that computer can understand. Binary numbers can be converted to decimal using binary to decimal conversion tools or by learning easy way to change binaries into decimals.
For learning how we can convert binary numbers to decimal numbers is so important as it will clear your idea on binary to decimal conversion manually without using any online based calculator.

Here I am explaining you a technique of how you can convert any binary to decimal number easily:
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REFERENCE LINK 1: BINARY 2 DECIMAL CONVERSION
DOWNLOAD: CONVERTER
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REFERENCE METHOD 2

  1. 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
  2. 2
    Write first the binary number below the list.
  3. 3
    Draw lines, starting from the right, connecting each consecutive digit of the binary number to the power of two that is next in the list above it. Begin by drawing a line from the first digit of the binary number to the first power of two in the list above it. Then, draw a line from the second digit of the binary number to the second power of two in the list. Continue connecting each digit with its corresponding power of two.
  4. 4
    Move through each digit of the binary number. If the digit is a 1, write its corresponding power of two below the line, under the digit. If the digit is a 0, write a 0 below the line, under the digit.
  5. 5
    Add the numbers written below the line. The sum should be 155. This is the decimal equivalent of the binary number 10011011. Or, written with base subscripts:
  6. 6
    Repetition of this method will result in memorization of the powers of two, which will allow you to skip step 1.

Doubling method

  1. 1
    This method does not use powers. As such, it is simpler for converting large numbers in your head because you only need to keep track of a subtotal.
  2. 2
    Start with the left-most digit of the given binary number. For each digit as you move to the right, double your previous total and add the current digit. For example, to convert 10110012 to decimal, we take the following steps:
  3. 3
    1011001 → 0 * 2 + 1 = 1
  4. 4
    1011001 → 1 * 2 + 0 = 2
  5. 5
    1011001 → 2 * 2 + 1 = 5
  6. 6
    1011001 → 5 * 2 + 1 = 11
  7. 7
    1011001 → 11 * 2 + 0 = 22
  8. 8
    1011001 → 22 * 2 + 0 = 44
  9. 9
    1011001 → 44 * 2 + 1 = 8910
  10. 10
    Like the positional notation method, this method can be modified to convert from any base to decimal. Doubling is used because the given number is of base 2. If the given number is of a different base, replace the 2 in the method with the base of the given number. For example, if the given number is in base 37, you would replace the *2 with *37. The final result will always be in decimal (base 10).

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