Lecture 23:- Number System - Binary && Decimal

Let's discuss the binary and decimal number systems:

Decimal Number System: The decimal number system, also known as the base-10 system, is the number system that we use in our daily lives. It uses ten digits (0 to 9) to represent numbers. In the decimal system, each digit's position represents a power of 10. The rightmost digit represents 10^0 (1), the next digit to the left represents 10^1 (10), the next one represents 10^2 (100), and so on.

For example:

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237 = (2 * 10^2) + (3 * 10^1) + (7 * 10^0) = 200 + 30 + 7

Binary Number System: The binary number system, also known as the base-2 system, is a number system used in digital electronics and computer programming. It uses two digits (0 and 1) to represent numbers. In the binary system, each digit's position represents a power of 2. The rightmost digit represents 2^0 (1), the next digit to the left represents 2^1 (2), the next one represents 2^2 (4), and so on.

For example:

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1011 (binary) = (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11 (decimal)

Converting Binary to Decimal: To convert a binary number to a decimal number, we multiply each binary digit by 2 raised to its corresponding power and sum the results.

Converting Decimal to Binary: To convert a decimal number to a binary number, we repeatedly divide the decimal number by 2 and note the remainder. The binary number is formed by reading the remainders in reverse order.

Here's an example of converting a decimal number to binary:

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Decimal number: 13 Step 1: 13 ÷ 2 = 6 with a remainder of 1 Step 2: 6 ÷ 2 = 3 with a remainder of 0 Step 3: 3 ÷ 2 = 1 with a remainder of 1 Step 4: 1 ÷ 2 = 0 with a remainder of 1 Binary number: 1101

Remember that the decimal system is the most familiar to us, while the binary system is essential in computer systems for representing data and performing computations at the hardware level. Understanding both number systems is crucial for understanding how computers process information.