by Binary arithmetic is a set of operations that are performed on binary numbers (numbers in base-2), which consist of only two digits: 0 and 1. These operations are fundamental to computer systems, as computers process all data in binary form. The basic operations of binary arithmetic include addition, subtraction, multiplication, and division.
1. Binary Addition
Binary addition follows the same principle as decimal addition, but it is simpler because it only involves two digits: 0 and 1. The basic rules for binary addition are:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (carry over the 1)
The carry-over in binary addition occurs when the sum of two bits equals 2 (which is written as “10” in binary).
2. Binary Subtraction
Binary subtraction follows the same rules as decimal subtraction. The basic rules for binary subtraction are:
- 0 – 0 = 0
- 0 – 1 = 1 (with a borrow)
- 1 – 0 = 1
- 1 – 1 = 0
When subtracting 1 - 0, the result is straightforward. However, when subtracting 0 - 1, we need to borrow from the next higher bit (just as in decimal subtraction).
3. Binary Multiplication
Binary multiplication is similar to decimal multiplication but follows simpler rules. The rules for binary multiplication are:
- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1
Multiplying binary numbers involves multiple steps, similar to long multiplication in decimal.
4. Binary Division
Binary division is similar to long division in the decimal system. The process involves dividing the binary dividend by the binary divisor, subtracting, and bringing down the next bit until the division is complete.
Significance of Binary Arithmetic in Computers
All operations performed in a computer, such as calculations, data manipulation, and logical operations, are based on binary arithmetic. Since computers operate using binary logic, these arithmetic operations are essential for:
- Arithmetic Logic Units (ALU): ALUs perform basic operations like addition, subtraction, multiplication, and division in a computer’s CPU.
- Data Storage: Data is stored and manipulated as binary values in memory.
- Program Execution: When a program is run, binary arithmetic is applied to process the instructions and perform the necessary tasks.
