What is the Difference Between Binary and Decimal?

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:

1. 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.
2. 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:

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.