- Binary Arithmetic Definition: Binary arithmetic uses only two numbers, 0 and 1, to perform operations like addition, subtraction, multiplication, and division.
- Binary Addition: Adds two binary numbers from the rightmost bit, carrying over when the sum at a bit is 2.
- Binary Subtraction: Involves borrowing from a more significant bit when subtracting a larger number from a smaller one at a specific bit.
- Binary Multiplication: Multiplication in binary follows a simplified process, multiplying each bit separately without carries or borrows.
- Binary Division: Uses both multiplication and subtraction techniques to determine the quotient and remainder.
The binary number system uses the digits 0 and 1. Arithmetic follows the same place-value principles used in decimal, with rules for binary addition, binary subtraction, binary multiplication and binary division.
For binary arithmetic, align the place values before calculating. Addition, subtraction and multiplication normally proceed from the rightmost column. Long division begins with the leftmost group that is large enough to contain the divisor.
Binary Addition
Binary addition uses these four one-bit rules:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 0 (carry 1 to the next column on the left)
For example, add binary 10001001 and 10010101 by aligning their rightmost digits and working one column at a time.
For this binary arithmetic example, the correct sum is 100011110. A carry of 1 moves into the next column on the left whenever a column total is 2 or 3.
Binary Subtraction
Binary subtraction uses these four one-bit rules:
- 0 – 0 = 0
- 0 – 1 = 1, after borrowing 1 from the next column on the left
- 1 – 0 = 1
- 1 – 1 = 0
The example subtracts binary 10100010 from 10101010. The result is 00001000, which equals decimal 8.
The binary subtraction image shows the operands aligned by place value and the eight-bit result.
Binary Multiplication
For binary multiplication, form one partial product for each multiplier bit. The one-bit multiplication rules are:
- 0×0=0
- 1×0=0
- 0×1=0
- 1×1=1
The image multiplies binary 1001 by 101. Its partial products add to 101101, which equals decimal 45.
Binary Division
Binary division compares the divisor with leading groups of the dividend. Each quotient bit determines whether to subtract a shifted copy of the divisor.
In the example, binary 11010 divided by 101 gives quotient 101 and remainder 1. In decimal, this is 26 divided by 5, giving quotient 5 and remainder 1.
