How would I write the binary number 11001 in decimal form? (2024)

Answer: 25. Explanation: In the binary system, each digit can be one of two values: 0 and 1. That's two possibilities ('bi' is Latin for 'twice'). In the decimal system, each digit can take any value from 0 to 9. That's ten possibilities ('decimus' is Latin for 'tenth'). In both systems, the value of 1 depends on which 'column' it occupies in a number. For example, staying with the decimal system, in the number 100, the 1 is in the hundreds column because it has two digits to the right of it (and no decimal point). Therefore, the 1 in this example represents the value of one hundred. This would be the same case in the number 146: the 1 still represents one hundred. We can generalise about the value of 1 in the decimal system: starting from the rightmost column, 1 represents the value of 10^0(=1); in the next column it represents 10^1(=10), in the third column it is 10^2(=100), and in the fourth column it is 10^3(=1000) etc. We can apply the same principle to the binary system: in the rightmost column, 1 represents 2^0(=1), in the second it is 2^1(=2), in the third it is 2^2(=4), in the fourth it is 2^3(=8), in the fifth it is 2^4(=16) etc. Therefore, 11001 (binary) is 1+8+16=25 (decimal).