In the following, write the binary number in base 10.
10110010
The binary number 10110010 is equal to 178 in base 10.
To convert the binary number 10110010 to base 10, follow these steps:
1. Assign powers of 2 to each digit in the binary number, starting from the rightmost digit. The rightmost digit is in position 0, the next one is in position 1, and so on.
2. Multiply each digit in the binary number by its corresponding power of 2.
3. Add up all the values obtained from step 2 to get the decimal equivalent of the binary number.
Let's calculate the decimal value of the binary number:
(1 * 2^7) + (0 * 2^6) + (1 * 2^5) + (1 * 2^4) + (0 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)
Simplifying the equation, we get:
(1 * 128) + (0 * 64) + (1 * 32) + (1 * 16) + (0 * 8) + (0 * 4) + (1 * 2) + (0 * 1)
128 + 0 + 32 + 16 + 0 + 0 + 2 + 0
Thus, the binary number 10110010 is equal to 178 in base 10.