How to Convert Binary to Decimal?

To convert a binary number to its decimal equivalent, multiply each digit by the corresponding power of 2 (starting from the rightmost digit as 2^0) and then sum the results.

Here's a step-by-step breakdown:

1. Identify the Binary Number: Determine the binary number you want to convert. For example, let's use the binary number 101101.

2. Assign Powers of 2: Assign each digit a power of 2, starting from the rightmost digit with 2⁰, then 2¹, 2², and so on.

   Binary Digit	Power of 2
   1	25
   0	24
   1	23
   1	22
   0	21
   1	20

3. Multiply Each Digit: Multiply each binary digit by its corresponding power of 2.

   • 1 2⁵ = 1 32 = 32
   • 0 2⁴ = 0 16 = 0
   • 1 2³ = 1 8 = 8
   • 1 2² = 1 4 = 4
   • 0 2¹ = 0 2 = 0
   • 1 2⁰ = 1 1 = 1

4. Sum the Results: Add up all the values calculated in the previous step.

   32 + 0 + 8 + 4 + 0 + 1 = 45

Therefore, the decimal equivalent of the binary number 101101 is 45.

Example 2:

Let's convert the binary number 11001 to decimal.

1. Assign powers of 2:

   Binary Digit	Power of 2
   1	24
   1	23
   0	22
   0	21
   1	20

2. Multiply:

   • 1 2⁴ = 1 16 = 16
   • 1 2³ = 1 8 = 8
   • 0 2² = 0 4 = 0
   • 0 2¹ = 0 2 = 0
   • 1 2⁰ = 1 1 = 1

3. Sum:

   16 + 8 + 0 + 0 + 1 = 25

Therefore, the decimal equivalent of the binary number 11001 is 25.

In summary, converting binary to decimal involves multiplying each binary digit by its corresponding power of 2 and summing the results to obtain the decimal representation.