100111101010

100111101010 is a binary number. In binary, each digit represents a power of two. The rightmost digit represents 2^0 (or 1), the next digit to the left represents 2^1 (or 2), and so on. To convert 100111101010 to its decimal (base-10) equivalent, we sum the powers of two where a '1' appears in the binary number.

Starting from the rightmost digit and moving left, the place values are 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7, 2^8, 2^9, 2^10, and 2^11. The binary number 100111101010 has '1's in the positions corresponding to 2^11, 2^8, 2^7, 2^6, 2^5, 2^3, and 2^1.

Calculating these powers of two:

2^11 = 2048

2^8 = 256

2^7 = 128

2^6 = 64

2^5 = 32

2^3 = 8

2^1 = 2

Summing these values gives: 2048 + 256 + 128 + 64 + 32 + 8 + 2 = 2538. Therefore, the binary number 100111101010 is equal to the decimal number 2538. This binary representation is commonly used in computer science and digital electronics for data storage and processing.