0110 in decimal

Understand the Problem

The question is asking to convert the binary number 0110 into its decimal equivalent. To do this, we will calculate the binary number by summing the powers of 2 for each digit that is '1'.

Answer

$6$

Steps to Solve

Identify the Binary Digits The binary number is 0110. It has four digits: 0, 1, 1, and 0.
Assign Powers of 2 From right to left, assign powers of 2 to each digit:

The rightmost digit (0) is $2^0$ (which equals 1)
The second digit (1) is $2^1$ (which equals 2)
The third digit (1) is $2^2$ (which equals 4)
The leftmost digit (0) is $2^3$ (which equals 8)

Calculate Contributions of Each Digit Now calculate the contribution to the decimal equivalent for each digit by multiplying the digit by its corresponding power of 2:

For the rightmost digit: $0 \cdot 2^0 = 0 \cdot 1 = 0$
For the second digit: $1 \cdot 2^1 = 1 \cdot 2 = 2$
For the third digit: $1 \cdot 2^2 = 1 \cdot 4 = 4$
For the leftmost digit: $0 \cdot 2^3 = 0 \cdot 8 = 0$

Sum the Contributions Add the contributions together to get the decimal equivalent: $$ 0 + 2 + 4 + 0 = 6 $$

The decimal equivalent of the binary number 0110 is $6$.

More Information

The binary number system is base-2, which means it only uses two digits: 0 and 1. Each position represents a power of 2, increasing as you move leftward. This system is widely used in computer science and digital electronics.

Tips

Forgetting to assign the correct powers of 2 to the digits
Miscalculating the contributions for each binary digit
Not summing the contributions correctly at the end

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