The binary calculation principle is based on the binary number system, which uses only two digits, 0 and 1.
Addition:
- In binary addition, the rules are similar to decimal addition but with only two digits to work with. For example, 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 (where the 1 is carried over to the next column).
- When adding multiple binary numbers, the process is the same as in decimal addition. Start from the rightmost column and add the digits in each column, carrying over if necessary.
Subtraction:
- Binary subtraction follows rules similar to decimal subtraction. For example, 0 - 0 = 0, 1 - 0 = 1, and 1 - 1 = 0. But when subtracting 1 from 0, a borrow is needed. For instance, 10 (binary 2) - 1 = 1.
- As with decimal subtraction, start from the rightmost column and subtract the digits in each column, borrowing if necessary.
Multiplication:
- Binary multiplication is simpler than decimal multiplication in some ways. Since there are only two digits, multiplying by 0 always results in 0, and multiplying by 1 results in the number being multiplied. For example, 1 x 1 = 1, 1 x 0 = 0, 0 x 1 = 0, and 0 x 0 = 0.
- To multiply two binary numbers, multiply each digit of one number by each digit of the other number and then add the results, taking care of any carries.
Division:
- Binary division is also similar to decimal division. For example, dividing 100 (binary 4) by 10 (binary 2) results in 10 (binary 2).
- The process involves repeated subtraction or a more formal division algorithm, similar to decimal division.
In general, binary calculations are performed using these basic operations. Computers use binary arithmetic because it is easier to implement electronically using switches that can be in either an on (1) or off (0) state.