Introduction-to-Binary-Arithmetic by Prince Singh roll no.-24.pptx
- 1. GARDENIA PUBLIC SCHOOL Summer holiday project Binary Arithmetic Operations Class:7th Su Subject : Computer Subject:Computer
- 2. Introduction to Binary Arithmetic Binary arithmetic is a system of mathematics that uses only two digits: 0 and 1. This system is fundamental to modern computing, as computers use binary to represent and process information.
- 3. Understanding Binary Numbers 1 Place Values Each position in a binary number represents a power of two, starting from the rightmost digit as 20, then 21, 22, and so on. 2 Base-2 System Binary numbers use base-2, meaning each digit can be either 0 or 1, unlike decimal numbers which use base-10 (0- 9). 3 Conversion to Decimal To convert a binary number to decimal, multiply each digit by its corresponding power of two and add the results. 4 Example The binary number 10112 is equivalent to 1*23 + 0*22 + 1*21 + 1*20 = 8 + 0 + 2 + 1 = 1110 in decimal.
- 4. Basic Binary Operations: Addition, Subtraction Binary Addition Similar to decimal addition, carry-overs occur when the sum of two digits exceeds 1. The carry-over is added to the next digit. 1. 0 + 0 = 0 2. 0 + 1 = 1 3. 1 + 0 = 1 4. 1 + 1 = 0 (carry-over 1) Binary Subtraction Borrowing is necessary when subtracting a larger digit from a smaller digit. The borrowing is done from the next digit, making it a 0 and adding 2 to the current digit. 1. 0 - 0 = 0 2. 1 - 0 = 1 3. 1 - 1 = 0 4. 0 - 1 = 1 (borrow 1)
- 5. Example: Adding Binary Numbers 10112 + 10012 ----- 101002
- 6. Example: Subtracting Binary Numbers 11012 - 10102 ----- 00112
- 7. Binary Multiplication and Division Multiplication Similar to decimal multiplication, binary multiplication involves multiplying each digit of the multiplicand by the multiplier and then adding the partial products. 1. 0 * 0 = 0 2. 0 * 1 = 0 3. 1 * 0 = 0 4. 1 * 1 = 1 Division Binary division works by repeatedly subtracting the divisor from the dividend until the remainder is less than the divisor.
- 8. Applications of Binary Arithmetic Digital Computers Computers rely on binary arithmetic to perform calculations, store data, and execute programs. Digital Logic Circuits Binary logic gates, such as AND, OR, and NOT, are built using binary arithmetic to process signals. Data Transmission Binary codes are used in communication networks to transmit digital information, ensuring accuracy and efficiency. Data Storage Binary codes are used in hard drives, flash drives, and other storage devices to represent data in a format that can be easily accessed by computers.
- 9. Conclusion Binary arithmetic is a foundational concept in computer science, providing the basis for how computers process and understand information. Its simplicity and efficiency make it essential for the operation of modern technology. The understanding of binary arithmetic is crucial for anyone seeking to delve deeper into the world of computing.