How to convert decimal number into binary number

The binary ("base two") numerical system has two possible values, often represented as 0 or 1, for each place-value. In contrast, the decimal (base ten) numeral system has ten possible values (0,1, 2, 3, 4, 5, 6, 7, 8, or 9) for each place-value. To avoid confusion while using different numeral systems, the base of each individual number may be specified by writing it as a subscript of the number. For example, the binary number 10011100 may be specified as "base two" by writing it as 10011100₂. The decimal number 156 may be written as 156₁₀ and read as "one hundred fifty-six, base ten". Since the binary system is the internal language of electronic computers, serious computer programmers should understand how to convert from binary to decimal. Converting in the opposite direction, from decimal to binary, is often more difficult to learn first.

METHODS 

1 Using positional notation 

Write down the binary number and list the powers of 2 from right to left.                                                                                 

Let's say we want to convert the binary number 10011011₂ to decimal. First, write it down.Then, write down 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, with eight elements, would look like this: 128, 64, 32, 16, 8, 4, 2, 1

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2. 2. Write the digits of the binary number below their corresponding powers of twoNow, just write 10011011 below the numbers 128, 64, 32, 16, 8, 4, 2, and 1 so that each binary digit corresponds with its power of two. The "1" to the right of the binary number should correspond with the "1" on the right of the listed powers of two, and so on. You can also write the binary digits above the powers of two, if you prefer it that way. What's important is that they match up.

   

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   2. 3. Connect the digits in the binary number with their corresponding powers of two. 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. This will help you visually see the relationship between the two sets of numbers.
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   Write down the final value of each power of two. 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.

   • Since "1" corresponds with "1", it becomes a "1." Since "2" corresponds with "1," it becomes a "2." Since "4" corresponds with "0," it becomes "0." Since "8" corresponds with "1", it becomes "8," and since "16" corresponds with "1" it becomes "16." "32" corresponds with "0" and becomes "0" and "64" corresponds with "0" and therefore becomes "0" while "128" corresponds with "1" and becomes 128.
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   Add the final values. Now, add up the numbers written below the line. Here's what you do: 128 + 0 + 0 + 16 + 8 + 0 + 2 + 1 = 155. This is the decimal equivalent of the binary number 10011011.
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   Write the answer along with its base subscript. Now, all you have to do is write 155₁₀, to show that you are working with a decimal answer, which must be operating in powers of 10. The more you get used to converting from binary to decimal, the more easy it will be for you to memorize the powers of two, and you'll be able to complete the task more quickly.
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   Use this method to convert a binary number with a decimal point to decimal form. You can use this method even when you want to covert a binary number such as 1.1₂ to decimal. All you have to do is know that the number on the left side of the decimal is in the units position, like normal, while the number on the right side of the decimal is in the "halves" position, or 1 x (1/2).

   • The "1" to the left of the decimal point is equal to 2₀, or 1. The 1 to the right of the decimal is equal to 2_-1, or .5. Add up 1 and .5 and you get 1.5, which is 1.1₂ in decimal notation.