Convert 111111 in base 2 to a number in base ten
To convert 111111 from base 2 to base 10, we need to use the positional value of each digit in base 2. The rightmost digit has a positional value of 2^0 (which is 1), and then each subsequent digit to the left has a positional value double the previous digit.
Therefore, the conversion would be as follows:
1 * 2^0 = 1
1 * 2^1 = 2
1 * 2^2 = 4
1 * 2^3 = 8
1 * 2^4 = 16
1 * 2^5 = 32
Adding up all the positional values, we get: 1 + 2 + 4 + 8 + 16 + 32 = 63
So, 111111 in base 2 is equal to 63 in base 10.
To convert the number 111111 from base 2 to base 10, you can use the positional notation method. Each digit in base 2 represents a power of 2. Let's break it down step-by-step:
1. Start from the rightmost digit, which is the least significant digit.
2. Multiply each digit by 2 raised to the power of its position. The position is counted from right to left, starting from 0.
For example, in the number 111111:
- The rightmost digit is 1, so we multiply it by 2^0 (which is 1), resulting in 1.
- The second rightmost digit is also 1, so we multiply it by 2^1 (which is 2), resulting in 2.
- Continuing this process for each digit from right to left, we get:
1 * (2^0) + 1 * (2^1) + 1 * (2^2) + 1 * (2^3) + 1 * (2^4) + 1 * (2^5)
3. Calculating the above expression will give us the decimal value of the number in base 10.
1 * 1 + 1 * 2 + 1 * 4 + 1 * 8 + 1 * 16 + 1 * 32 = 63
Therefore, the number 111111 in base 2 is equal to 63 in base 10.