How do you convert binary to decimal?
Understand the Problem
The question is asking for a method or explanation on how to convert a number from binary (base-2) format to decimal (base-10) format, which involves understanding the place value of binary digits.
Answer
13
Answer for screen readers
So, the decimal equivalent of the binary number 1101
is 13.
Steps to Solve
- Identify the binary number
Carefully note down the given binary number. For example, let's take the binary number 1101
.
- Assign place values to each binary digit
Each binary digit (bit) has a place value that is a power of 2, starting from the rightmost bit (which has a place value of $2^0$). For the binary number 1101
, the place values are:
[ 1 \times 2^3, 1 \times 2^2, 0 \times 2^1, 1 \times 2^0 ]
- Calculate each term's value
Multiply each binary digit by its corresponding place value:
[ 1 \times 2^3 = 8 ] [ 1 \times 2^2 = 4 ] [ 0 \times 2^1 = 0 ] [ 1 \times 2^0 = 1 ]
- Sum all the terms
Add the results from the previous step to get the decimal value:
[ 8 + 4 + 0 + 1 = 13 ]
So, the decimal equivalent of the binary number 1101
is 13.
So, the decimal equivalent of the binary number 1101
is 13.
More Information
Binary to decimal conversion is a fundamental concept in computer science and digital electronics.
Tips
Common mistakes include incorrectly assigning place values or forgetting to multiply the binary digit by its corresponding power of 2.