How to Convert from Binary to Decimal如何從二進制轉換為十進制

The binary ( base two ) numeral system has two possible values, often represented as 0 or 1, for each place-value. 二進制 （基2 ） 數字系統有兩個可能的值，往往是派0或1 ，為每個位置的價值。 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.與此相反， 十進制 （基10 ） 數字系統有10個可能的值（ 0,1,2,3,4,5,6,7,8 ，或9 ）為每個位置的價值。

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.為了避免混亂而採用不同的數字系統，基地每個號碼可以以書面形式指定它作為標數量。 For example, the binary number 10011100 may be specified as “base two” by writing it as 10011100 ₂ .例如，二進制數一千零一點一一萬可能被指定為“兩基”的書面它作為10011100 _{2 。} The decimal number 156 may be written as 156 ₁₀ and read as “one hundred fifty-six, base ten”.十進制數的156可寫成156 ₁₀改為“ 156 ，基地10個。 ”

Since the binary system is the internal language of electronic computers, serious computer programmers should understand how to convert from binary to decimal.由於二元體系是內部語言的電子計算機，嚴重的計算機程序員應該懂得如何從二進制轉換為十進制。 Converting in the opposite direction, from decimal to binary, is often more difficult to learn first.轉換相反的方向，從十進制的二進制，往往更難以學習第一。

Note: This is ONLY for counting and does not talk about ASCII translations.注意：這僅僅是算不談論的ASCII翻譯。

1. For this example, let’s convert the binary number 10011011 ₂ to decimal.在這個範例中，讓我們轉換成二進制數10011011 _2至小數。 List the powers of two from right to left.清單的權力，兩個從右到左。 Start at 2 ⁰ , evaluating it as “1″.開始於² 0 ，評價為“ 1 ” 。 Increment the exponent by one for each power.增量指數的一個，每個權力。 Stop when the amount of elements in the list is equal to the amount of digits in the binary number.停止時的數額中的元素清單的數額相等數字的二進制數。 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範例號碼， 10011011 ，有8位數字，因此，清單中， 8個要素，將看起來就像這樣： 128 ， 64 ， 32 ， 16 ， 8 ， 4 ， 2 ， 1
2. Write the binary number below the list.收件的二進制數低於名單。
   

   Here is this step written on paper using the example binary number, 10011011.以下是這一步寫在紙上的使用例如二進制數， 10011011 。
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.繪製線條，從權，連接每個連續兩位數的二進制數的權力，這是兩國今後在名單之上。 Begin by drawing a line from the first digit of the binary number to the first power of two in the list above it.首先，畫線從第一位數的二進制數的第一個電源的兩個清單中的上面。 Then, draw a line from the second digit of the binary number to the second power of two in the list.然後，畫一條線從第二位的二進制數的第二個電源的兩個清單中。 Continue connecting each digit with its corresponding power of two.繼續連接每個數字與其相應的權力兩項。
   

   Here is this step written on paper using the example binary number, 10011011.以下是這一步寫在紙上的使用例如二進制數， 10011011 。
4. Move through each digit of the binary number.通過每一個移動數字的二進制數。 If the digit is a 1, write its corresponding power of two below the line, under the digit.如果數字是1 ，寫其相應的權力低於兩線，根據位數。 If the digit is a 0, write a 0 below the line, under the digit.如果數字是0 ，寫一0線以下，根據位數。
   

   Here is this step written on paper using the example binary number, 10011011.以下是這一步寫在紙上的使用例如二進制數， 10011011 。
5. Add the numbers written below the line.購買的數量低於書面線。 The sum should be 155.該金額應155 。 This is the decimal equivalent of the binary number 10011011.這是小數相當於二進制數10011011 。 Or, written with base subscripts: 10011011 ₂ = 155 ₁₀或者，與基地的書面標： 10011011 _{2 =} 155 _10個
   

   Here is this step written on paper using the example binary number, 10011011.以下是這一步寫在紙上的使用例如二進制數， 10011011 。 The sum of the bottom row, 155, is its decimal equivalent.之行的底部， 155 ，是它的小數點當量。 Or, written with base subscripts: 10011011 ₂ = 155 ₁₀或者，寫基地標： 10011011 _{2 =} 155 _10個
6. Repetition of this method will result in memorization of the powers of two, which will allow you to skip step 1.重複這一方法會導致記憶力的權力兩個，這將允許您跳過步驟1 。

Doubling Method: 倍頻方法：

Starting from zero, and working from left to right, double your number and add the next digit of the base two representation.從零開始，工作從左至右，雙擊您的電話號碼，並新增未來兩位數的基礎兩個代表性。 For example to convert 1011001, we take the following steps.例如轉換1011001 ，我們採取以下步驟。

1. 1|011001 0*2+1 = 1 1 | 011001 0 * 2 +1 = 1
2. 10|11001 1*2+0 = 2 10 | 11001 1 * 2 +0 = 2
3. 101|1001 2*2+1 = 5 101 | 1001 ， 2 * 2 +1 = 5
4. 1011|001 5*2+1 = 11 1011 | 001 5 * 2 +1 = 11
5. 10110|01 11*2+0 = 22 1.011萬| 1月11日* 2 +0 = 22
6. 101100|1 22*2+0 = 44 101100 | 1月22日* 2 +0 = 44
7. 1011001 44*2+1 = 89 1011001 44 * 2 +1 = 89