Converting Binary to Decimal

What you'll learn: How to translate binary numbers into everyday decimal numbers using the place-value method.

Understanding Place Values

You already know how to count in binary (0, 1, 10, 11, 100...), but how do we figure out what those binary numbers mean in our familiar decimal system?

Think about how regular decimal numbers work. In the number 247, each digit has a place value:

• 2 is in the "hundreds" place (2 × 100 = 200)
• 4 is in the "tens" place (4 × 10 = 40)
• 7 is in the "ones" place (7 × 1 = 7)
• Total: 200 + 40 + 7 = 247

Binary works exactly the same way, except instead of powers of 10 (100, 10, 1), we use powers of 2 (8, 4, 2, 1).

The Place-Value Method

Let's convert the binary number 1011 to decimal:

Step 1: Write the place values from right to left:

1    0    1    1
8    4    2    1  ← place values (powers of 2)

Step 2: Multiply each binary digit by its place value:

• 1 × 8 = 8
• 0 × 4 = 0
• 1 × 2 = 2
• 1 × 1 = 1

Step 3: Add them all up: 8 + 0 + 2 + 1 = 11

So binary 1011 equals decimal 11.

Another Example

Binary 100101:

1     0     0     1     0     1
32    16    8     4     2     1

(1×32) + (0×16) + (0×8) + (1×4) + (0×2) + (1×1) = 32 + 4 + 1 = 37

Key Takeaway: To convert binary to decimal, multiply each digit by its place value (powers of 2, from right to left: 1, 2, 4, 8, 16...), then add the results together.