0111 in decimal
Understand the Problem
The question is asking for the decimal equivalent of the binary number 0111. To convert a binary number to decimal, we sum up the values of the bits that are set to 1, taking into account their positional value based on powers of 2.
Answer
$7$
Answer for screen readers
The decimal equivalent of the binary number $0111$ is $7$.
Steps to Solve
- Identify the binary digits and their positions
The binary number 0111 has four digits. We can label their positions from right to left starting at 0:
- Position 0: 1 (the rightmost digit)
- Position 1: 1
- Position 2: 1
- Position 3: 0
- Calculate the decimal value of each bit
Each bit has a value of $2^n$, where $n$ is the position of the bit:
- Position 0: $2^0 \cdot 1 = 1$
- Position 1: $2^1 \cdot 1 = 2$
- Position 2: $2^2 \cdot 1 = 4$
- Position 3: $2^3 \cdot 0 = 0$
- Sum the values of the bits that are set to 1
Now add these calculated values:
$$ 1 + 2 + 4 + 0 = 7 $$
The decimal equivalent of the binary number $0111$ is $7$.
More Information
The binary number system is base-2, meaning it consists of only two digits: 0 and 1. Each position represents a power of 2. Converting binary numbers is essential in computer science, as computers operate primarily using binary code.
Tips
- Forgetting to begin counting positions from 0. Always start from the rightmost digit as position 0.
- Miscalculating the power of 2 for each bit; ensure to apply the exponent correctly based on the bit's position.
