How to Convert Binary to Decimal with 7 Examples

In the digital world, computers use the binary system, which consists of only two digits: 0 and 1. In contrast, humans primarily utilize the decimal system, with ten digits from 0 to 9.

Converting binary numbers to decimal allows us to interpret and work with binary data in a format that is more familiar to us.

It is an essential skill for programmers, computer scientists, and anyone dealing with binary data.

Understanding Binary and Decimal Number Systems

Before we dive into the conversion process, let’s gain a basic understanding of the binary and decimal number systems.

In the decimal system, each digit’s place value represents a power of 10. The rightmost digit corresponds to $10^0$ (1), the next digit represents $10^1$ (10), followed by $10^2$ (100), and so on.

In binary, the place values are powers of 2. The rightmost digit represents $2^0$ (1), the next digit represents $2^1$ (2), then $2^2$ (4), and so forth.

How to Convert Binary to Decimal Step-by-Step

Now, let’s look at the step-by-step process of converting binary numbers to decimal.

Step 1: Assigning Place Values

Begin by assigning place values to each digit in the binary number, starting from the rightmost digit.

The rightmost digit will have a place value of $2^0$ (1), the next digit to the left will have a place value of $2^1$ (2), the next digit will have $2^2$ (4), and so on.

Step 2: Calculating the Decimal Equivalent

Multiply each digit in the binary number by its corresponding place value and sum up the results. This calculation will give you the decimal equivalent of the binary number.

Step 3: Finalizing the Conversion

After calculating the decimal equivalent, you have successfully converted the binary number to decimal.

The decimal number represents the same value as the original binary number but in the decimal number system.

Examples of How to Convert a Binary Number to Decimal

Example 1: Convert the binary number, 10110 to decimal

Step 1: Assigning Place Values:

  1        0        1        1        0

2^4   2^3   2^2   2^1   2^0
16      0       4        2        0


Step 2: Calculating the Decimal Equivalent:

1 * 16 + 0 * 0 + 1 * 4 + 1 * 2 + 0 * 1 = 22


Therefore, the binary number, 10110 is equal to 22 in decimal.

Example 2: Convert the binary number, 110011 to decimal.

Step 1: Assigning Place Values:

 1        1        0        0        1        1

2^5   2^4   2^3   2^2   2^1   2^0
32      16      0       0       2       1


Step 2: Calculating the Decimal Equivalent:

1 * 32 + 1 * 16 + 0 * 0 + 0 * 0 + 1 * 2 + 1 * 1 = 51


Hence, the binary number, 110011 is equal to 51 in decimal.

Example 3: Convert the Binary 1101 to Decimal

Step 1: Assigning Place Values:

1        1        0        1

2^3   2^2   2^1   2^0
8       4       0       1


Step 2: Calculating the Decimal Equivalent:

1 * 8 + 1 * 4 + 0 * 0 + 1 * 1 = 13


Therefore, the binary number 1101 is equal to 13 in decimal.

Example 4: Convert the Binary 10010 to Decimal

Step 1: Assigning Place Values:

1        0        0        1        0

2^4   2^3   2^2   2^1   2^0
16      0       0       2       0


Step 2: Calculating the Decimal Equivalent:

1 * 16 + 0 * 0 + 0 * 0 + 1 * 2 + 0 * 1 = 18


Hence, the binary number 10010 is equal to 18 in decimal.

Example 5: Convert the Binary 111111 to Decimal

Step 1: Assigning Place Values:

1        1        1        1        1        1

2^5   2^4   2^3   2^2   2^1   2^0
32      16      8        4       2       1


Step 2: Calculating the Decimal Equivalent:

1 * 32 + 1 * 16 + 1 * 8 + 1 * 4 + 1 * 2 + 1 * 1 = 63


Therefore, the binary number 111111 is equal to 63 in decimal.

Example 6: Converting Binary 10101 to Decimal

Step 1: Assigning Place Values:

1        0        1        0        1

2^4   2^3   2^2   2^1   2^0
16      0     4     0     1


Step 2: Calculating the Decimal Equivalent:

1 * 16 + 0 * 0 + 1 * 4 + 0 * 0 + 1 * 1 = 21


Hence, the binary number 10101 is equal to 21 in decimal.

Example 7: Convert the Binary, 1100100 to Decimal

Step 1: Assigning Place Values:

1        1        0        0        1        0        0

2^6   2^5   2^4   2^3   2^2   2^1   2^0
64      32      0       0       4       2       0


Step 2: Calculating the Decimal Equivalent:

1 * 64 + 1 * 32 + 0 * 0 + 0 * 0 + 1 * 4 + 0  *2 + 0*  1 = 100


Therefore, the binary number, 1100100 is equal to 100 in decimal.

Advantages of Binary and Decimal Number Systems

Both the binary and decimal number systems have their unique advantages. The binary system is the foundation of modern digital computing, as it aligns with the electronic nature of computers.

It enables efficient storage and manipulation of data in digital devices. On the other hand, the decimal system is more suitable for human comprehension, making it ideal for everyday calculations, financial transactions, and general mathematics.

Wrap Up

Converting binary numbers to decimal is a crucial skill for understanding and working with binary data.

By following the step-by-step process we discussed, you can easily convert binary numbers to their decimal equivalents.

Remember that the binary system represents data using two digits (0 and 1), while the decimal system uses ten digits (0 to 9).

Developing proficiency in this conversion process will empower you to perform various computations and solve problems in the digital realm.