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Learn Binary to Decimal Conversion Using Two Methods
It is important to learn how to convert a value from one number system to another number system as this enables us to tell when the two values with different numeral systems represent a similar amount. In the conversion of Binary to Decimal, we convert base 2 numbers to base 10 numbers using a binary to the decimal method. For example, if the binary number is (1011)₂ then the value of its equivalent decimal would be (11)10. Read on to know the method to convert binary to decimal numbers.
Methods to Convert Binary Numbers to Decimal Numbers
Binary numbers can be converted into decimal numbers using 2 methods namely:
- Positional Method
- Doubling Method
Positional Method to Convert Binary Numbers to Decimal Numbers
Following are the steps to convert binary numbers to decimal numbers using the positional method:
Let us convert the binary number (0100110)₂ to its equivalent decimal value.
Step 1: Starting from the right side, write down each digit of the given binary number by the increasing power of 2. Here, the first power would be 2⁰. As we move forward, the power will increase by 1. For example, the powers for the next digits will be 2¹, 2²,2³,2⁴, 2⁵,2⁶, and so on. In the given binary number there are 7 digits, hence, the weight of each digit from the rightmost position will be
0 = 2⁰
1= 2¹
1 = 2²
0 = 2³
0 = 2⁴
1= 2⁵
0 = 2⁶
Step 2: Starting from the rightmost position, multiply each digit with its respective weight based on its position and evaluate the product. Further, sum up all the products obtained for all the digits in the binary number as shown below.
(0 2¹) + (1 2¹) + (1 2²) + (0 2³) + (0 2⁴) + (1 2⁵) + (0 2⁶)
= 0 + 2 + 4 + 0 + 0 + 32 + 0
= (38)10
With this, we get the equivalent decimal value of the binary number (0100110)₂.
Therefore, (0100110)₂.= (38)0
Doubling Method to Convert Binary Numbers to Decimal Numbers
Following are the steps to convert binary numbers to decimal numbers using the doubling method:
- Write down the given binary number.
- Starting from the left-most digit, double the previous digit and add the current digit. As we first observe the left-most digit, there is no previous digit to the left-most digit. Accordingly, we can consider the double of the previous digit as 0. For example:
In (101101), the left-most digit is 1, and there is no previous digit. Therefore, the double of the previous digit here will be 0. Accordingly, we get (0 2) + 1 = 1.
- Continue the same process for the second digit also. The second digit is 0. Here, if we double the previous digit, we will get (1 + 1= 2). Now, if we add this double of the previous to the current digit, we get 2 + 0 = 2.
- Continue the same steps with all the remaining digits. The sum you receive at the last will be considered as the decimal value. Therefore, the equivalent decimal value for the given binary number (101101)₂would be (45)
Hope you understood both the methods discussed above. Visit Cuemath to practice more and more questions related to binary to decimal conversion using the methods discussed above.
