Understanding Binary and Decimal Conversions

Categories binary decimal conversions number systems

In the realm of number systems, the most common are binary and decimal. The binary system, which uses only two digits (0 and 1), is the foundation of modern computing. In contrast, the decimal system is based on ten digits (0-9), which is what we use in everyday life.

Binary to Decimal Conversion

To convert a binary number to decimal, you need to understand the positional value of each digit. For example, the binary number 1011 can be converted to decimal by calculating:

• 1 × 2³ = 8
• 0 × 2² = 0
• 1 × 2¹ = 2
• 1 × 2⁰ = 1

Adding these values together gives you 11 in decimal.

Decimal to Binary Conversion

To convert a decimal number to binary, you can use the method of repeated division by 2. For instance, to convert 11 to binary:

• 11 ÷ 2 = 5 remainder 1
• 5 ÷ 2 = 2 remainder 1
• 2 ÷ 2 = 1 remainder 0
• 1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top gives you 1011.

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