100001101001001

100001101001001 is a binary number. In the decimal system, it represents the value 67177. Binary is a base-2 numeral system, meaning it uses only two symbols, typically 0 and 1. Each digit in a binary number represents a power of 2, starting from 2^0 on the rightmost side.

To convert 100001101001001 from binary to decimal, we can assign weights to each digit based on its position. Starting from the rightmost digit (position 0) and moving left:

1 * 2^0 = 1

0 * 2^1 = 0

0 * 2^2 = 0

1 * 2^3 = 8

0 * 2^4 = 0

0 * 2^5 = 0

1 * 2^6 = 64

1 * 2^7 = 128

0 * 2^8 = 0

0 * 2^9 = 0

0 * 2^10 = 0

0 * 2^11 = 0

0 * 2^12 = 0

0 * 2^13 = 0

1 * 2^14 = 16384

Summing these values: 1 + 8 + 64 + 128 + 16384 = 16585. There was a miscalculation in the initial decimal representation. The correct decimal conversion of 100001101001001 is 16585.

Binary numbers are fundamental to computing, as they are the language that computers understand. Electrical circuits within computers can easily represent two states, often referred to as "on" and "off," which directly correspond to the binary digits 1 and 0. This binary representation is used for all data, including numbers, text, images, and instructions.

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