To convert a binary number to a decimal number, we use the concept of place values. In the binary system (base 2), each digit's place value is a power of 2. Starting from the rightmost digit (the least significant bit), the place values are $2^0, 2^1, 2^2$, and so on, increasing by one for each position to the left.

The given binary number is (11101011)₂.

Let's list the digits and their corresponding place values (powers of 2):

To find the decimal equivalent, we multiply each binary digit by its corresponding place value (power of 2) and then sum up all the results. Remember, any power of 2 multiplied by 0 will be 0.

Let's calculate the powers of 2:

• $2^0 = 1$
• $2^1 = 2$
• $2^2 = 4$
• $2^3 = 8$
• $2^4 = 16$
• $2^5 = 32$
• $2^6 = 64$
• $2^7 = 128$

Now, let's perform the multiplication and summation for the binary number (11101011)₂:

$$(11101011)_2 = (1 \times 2^7) + (1 \times 2^6) + (1 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0)$$ $$= (1 \times 128) + (1 \times 64) + (1 \times 32) + (0 \times 16) + (1 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1)$$ $$= 128 + 64 + 32 + 0 + 8 + 0 + 2 + 1$$ $$= 235$$

So, the binary number (11101011)₂ is equal to 235 in the decimal system.

Revision Table: Binary to Decimal Conversion

Additional Information: Number Systems

Understanding different number systems like binary and decimal is fundamental in computing and mathematics. Here's a brief overview:

• Binary System (Base 2): Uses only two digits, 0 and 1. It's the native language of computers because it can be easily represented by electrical states (on/off, high/low voltage).
• Decimal System (Base 10): Uses ten digits, 0 through 9. This is the number system we use in our everyday lives.
• Place Value: In any number system, the position of a digit determines its value. This value is the digit multiplied by the base raised to the power of its position (starting from 0 on the right).
• Other Systems: Other common number systems include Octal (base 8, digits 0-7) and Hexadecimal (base 16, digits 0-9 and A-F). These are often used in computing as a shorthand for binary numbers. Converting between these bases and decimal follows similar principles of place value.