Please convert the binary number 1000 to base 10
To convert the binary number 1000 to base 10, we need to start from the rightmost digit and multiply each digit by 2 raised to the power of its position.
1000 = (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (0 * 2^0)
= 8 + 0 + 0 + 0
= 8
So, the binary number 1000 is equal to the decimal number 8.
To convert a binary number to base 10, you can use the positional system, where each digit's value is determined by its position.
To convert the binary number 1000 to base 10, follow these steps:
Step 1: Write down the binary number: 1000.
Step 2: Assign each digit a positional value. For binary, the rightmost digit has a positional value of 2^0, the second digit from the right has a positional value of 2^1, then 2^2, and so on.
In this case:
- The rightmost digit is 0, so its positional value is 2^0 = 1.
- The second digit from the right is 0, so its positional value is 2^1 = 2.
- The third digit from the right is 0, so its positional value is 2^2 = 4.
- The leftmost digit is 1, so its positional value is 2^3 = 8.
Step 3: Multiply each digit by its positional value.
In this case:
- 0 x 1 = 0
- 0 x 2 = 0
- 0 x 4 = 0
- 1 x 8 = 8
Step 4: Add the products from Step 3.
In this case: 0 + 0 + 0 + 8 = 8.
Therefore, the binary number 1000 is equal to the base 10 number 8.
To convert a binary number to base 10, you need to multiply each digit of the binary number by the corresponding power of 2 and then sum up the results.
Let's convert the binary number 1000 to base 10:
Start by writing down the binary number: 1000
Now, we will assign powers of 2 to each digit from right to left. The rightmost digit is in the 0th position, and each subsequent digit has its power of 2 increased by 1.
1000
---->
2^3 2^2 2^1 2^0
Now, multiply each digit of the binary number by its corresponding power of 2:
(1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (0 * 2^0)
Simplifying this expression, we get:
(1 * 8) + (0 * 4) + (0 * 2) + (0 * 1)
Which equals:
8 + 0 + 0 + 0
Therefore, the binary number 1000 is equal to 8 in base 10.