Binary and Decimal Conversion

Binary and Decimal Description

Binary System:

• Description: The binary system is a base-2 numeral system that uses only two symbols: typically 0 and 1. It is the fundamental language of computers, where data is processed and stored using combinations of these two states.
• Basic Use: Binary is used in digital electronics and computing to represent and process all kinds of data and instructions. Everything from simple numeric data to complex multimedia content is ultimately represented in binary form in computers.

Decimal System:

• Description: The decimal system, also known as the base-10 system, is the most commonly used numeral system, especially in everyday counting and arithmetic. It uses ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
• Basic Use: The decimal system is used in most human-oriented applications, including general mathematics, finance, and most daily contexts where numbers are used.

Conversion from Binary to Decimal

To convert a binary number to decimal:

1. List the Powers of 2: Write down the powers of 2 from right to left. Start from 2^0, then 2^1, 2^2, and so on. Each power of 2 aligns with a digit in the binary number.
2. Multiply and Sum: Multiply each binary digit by its corresponding power of 2. Then, sum all the resulting products to get the decimal equivalent.

For example, to convert the binary number 1101 to decimal:

• (1 × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0)
• 8 + 4 + 0 + 1 = 13

So, 1101 in binary equals 13 in decimal.

Conversion from Decimal to Binary

To convert a decimal number to binary:

1. Divide by 2: Divide the decimal number by 2.
2. Write Down the Remainder: Record the remainder (it will be either 0 or 1).
3. Repeat: Repeat the division with the quotient obtained until the quotient becomes 0.
4. Read the Remainders in Reverse: The binary number is formed by the remainders, read from bottom to top.

For example, to convert the decimal number 13 to binary:

• 13 ÷ 2 = 6 remainder 1
• 6 ÷ 2 = 3 remainder 0
• 3 ÷ 2 = 1 remainder 1
• 1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top, we get 1101.

So, 13 in decimal equals 1101 in binary.

Application

Understanding binary and decimal systems is crucial in computing and electronics, as they form the basis of data representation and processing. Additionally, the ability to convert between these two systems is important in fields like computer science, engineering, and information technology.

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