Binary 100 Decimal Conversion

This explanation details how to find the decimal equivalent of the binary number 100.

Understanding Number Systems

Computers use the binary system (base-2), which only uses digits 0 and 1. Humans commonly use the decimal system (base-10), which uses digits 0 through 9. Converting between these systems is a fundamental concept in digital electronics and computer science.

Converting Binary to Decimal

To convert a binary number to its decimal equivalent, we multiply each binary digit by its corresponding positional weight (a power of 2) and sum the results. The positional weights increase from right to left, starting with $2^0$.

Step-by-Step Calculation

Let's convert the binary number 100:

1. Identify the binary digits and their positions. The number is 100.
2. Assign positional weights (powers of 2) starting from the rightmost digit:
   • The rightmost digit (0) is in the $2^0$ position.
   • The middle digit (0) is in the $2^1$ position.
   • The leftmost digit (1) is in the $2^2$ position.
3. Multiply each digit by its positional weight:
   • Leftmost digit: $1 \times 2^2$
   • Middle digit: $0 \times 2^1$
   • Rightmost digit: $0 \times 2^0$
4. Calculate the values:
   • $1 \times 2^2 = 1 \times 4 = 4$
   • $0 \times 2^1 = 0 \times 2 = 0$
   • $0 \times 2^0 = 0 \times 1 = 0$
5. Sum the results: $4 + 0 + 0 = 4$.

Positional Value Table

Here's a table summarizing the conversion:

Conclusion

Therefore, the decimal equivalent of the binary number 100 is 4.