Introduction_to_Base10_and_Base2_Number_Systems.pptx

number systems

1. Introduction to Number Systems: Base 10 and Base 2 Understanding Decimal and Binary Systems with Conversion Examples

2. What is a Number System? A number system is a writing system for expressing numbers. It is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

3. Base 10 (Decimal) Number System The decimal number system, also known as base 10, is the standard system for denoting integer and non-integer numbers. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

4. Base 2 (Binary) Number System The binary number system, also known as base 2, is used internally by almost all modern computers and computer-based devices. It uses only two digits: 0 and 1.

5. Converting from Decimal to Binary To convert a decimal number to binary: 1. Divide the decimal number by 2. 2. Write down the remainder (0 or 1). 3. Divide the quotient by 2. 4. Repeat steps 2 and 3 until the quotient is 0. 5. The binary number is the sequence of remainders read from bottom to top.

6. Example: Decimal to Binary Conversion Convert decimal number 25 to binary: 25 ÷ 2 = 12 remainder 1 12 ÷ 2 = 6 remainder 0 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Binary representation of 25 is read from bottom to top: 11001

7. Converting from Binary to Decimal To convert a binary number to decimal: 1. Write down the binary number. 2. Starting from the right, multiply each binary digit by 2 raised to the power of its position. 3. Sum all the products.

8. Example: Binary to Decimal Conversion Convert binary number 11001 to decimal: (1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0) = (16) + (8) + (0) + (0) + (1) = 25 Decimal representation of binary number 11001 is: 25

9. Conclusion Understanding base 10 and base 2 number systems is fundamental in digital electronics and computer science. The ability to convert between these systems allows for better comprehension of how computers process and store data.