What is the Difference Between Binary and Decimal?
🆚 Go to Comparative Table 🆚The main difference between binary and decimal lies in the base or radix they use to represent numbers. Binary and decimal number systems differ in the following aspects:
- Base: Binary is a base-2 number system, meaning it uses only two digits (0 and 1) to represent values. In contrast, decimal is a base-10 number system, which uses ten digits (0-9) to represent values.
- Representation: Binary numbers are represented in terms of powers of 2, while decimal numbers are represented in terms of powers of 10.
- Digits: Binary numbers can only be expressed using the digits 0 and 1, whereas decimal numbers can be expressed using the digits 0-9.
Conversion between binary and decimal:
- Binary to Decimal: To convert a binary number into a decimal number, multiply each digit of the binary number by the power of 2 that corresponds to its position. Then, sum up these products to get the decimal number.
- Decimal to Binary: To convert a decimal number into binary, repeatedly divide the number by 2 until the result is 0. Record the remainder of each division as a binary digit (bit) and continue the process until the result is 0.
For example, to convert the binary number 1011 to decimal, it would be calculated as follows: $$1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 11$$ and in the opposite direction, to convert the decimal number 11 to binary, it would be calculated as follows: $$\frac{11}{2} = 5 \text{ (remainder 1)}$$ $$\frac{5}{2} = 2 \text{ (remainder 1)}$$ $$\frac{2}{2} = 1 \text{ (remainder 0)}$$ so 11 in binary is 1011.
Comparative Table: Binary vs Decimal
The main difference between binary and decimal number systems lies in the base or radix they use to represent numbers. Here is a table summarizing the differences between binary and decimal:
Feature | Binary | Decimal |
---|---|---|
Base | 2 | 10 |
Symbols | 0, 1 | 0-9 |
Usage | Commonly used in computer systems and electronics | Less used in computer systems, more prevalent in everyday life |
The binary number system uses only two digits, 0 and 1, to represent numbers. In contrast, the decimal number system uses digits from 0 to 9 to represent numbers. Binary numbers are commonly used in computer systems and electronics, while decimal numbers are less used in computer systems but more prevalent in everyday life.
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