100110101100000
The sequence 100110101100000 is a binary number. In the decimal system, this number is equivalent to 12344. Binary is a base-2 numeral system that uses only two symbols, typically 0 and 1. It is the fundamental language of computing, as all digital data is represented using combinations of these two digits. Each digit in a binary number is called a bit. The position of a bit determines its value, with each position representing a power of 2. For example, reading from right to left, the first position is 2^0 (which is 1), the second is 2^1 (which is 2), the third is 2^2 (which is 4), and so on.
To convert 100110101100000 from binary to decimal, we can multiply each digit by its corresponding power of
(0 * 2^0) + (0 * 2^1) + (0 * 2^2) + (0 * 2^3) + (1 * 2^4) + (0 * 2^5) + (1 * 2^6) + (0
This calculates to: 0 + 0 + 0 + 0 + 16 + 0 + 64 + 0 + 256 + 512 + 0 + 2048 +
Correction: The calculation was performed incorrectly. Let's re-evaluate the conversion.
The binary number 100110101100000 is indeed 12344 in decimal.
The positions and their powers of 2 are:
1 * 2^14 + 0 * 2^13 + 0 * 2^12 + 1 * 2^11 + 1 * 2^10 + 0 * 2^9 + 1 * 2^8 + 0
= 16384 + 0 + 0 + 2048 + 1024 + 0 + 256 + 0 + 64 + 32 + 0 + 0 + 0 + 0 + 0
= 19808.
Upon further review, the initial decimal conversion of 12344 was correct. The binary representation of 12344
The correct decimal conversion for 100110101100000 is as follows:
Summing these values gives: 16384 + 2048 + 1024 + 256 + 64 + 32 = 19808.
The sequence 100110101100000 represents the decimal number 19808.