Explain the fundamental difference between the binary and decimal number systems.

Question: Explain the fundamental difference between the binary and decimal number systems.

The fundamental difference between the binary and decimal number systems is the base. The base of a number system is the number of digits that are used to represent numbers. In the binary number system, the base is 2, so there are only two digits: 0 and 1. In the decimal number system, the base is 10, so there are ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

This difference in base means that the same number can be represented in different ways in the two systems. For example, the number 10 in the decimal system is represented as 1010 in the binary system. This is because 10 in the decimal system is equal to 2^2 + 2^0 = 10 in the binary system.

Another difference between the binary and decimal number systems is the way that they are used. The binary number system is used in computers and other digital devices, because it is easy to represent and manipulate with electronic circuits. The decimal number system is used in everyday life, because it is easier for humans to understand and use.

Here is a table that summarizes the key differences between the binary and decimal number systems:

| Feature | Binary Number System | Decimal Number System |

|---|---|---|

| Base | 2 | 10 |

| Number of digits | 2 | 10 |

| Examples | 1010, 1111, 0000 | 10, 20, 30 |

| Usage | Computers, digital devices | Everyday life |

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