Binary arithmetic operations

• In mathematics, the four basic arithmetic operations applied on numbers are addition, subtraction, multiplications and division.
• In computers, the same operations are performed inside the central processing unit by the arithmetic and logic unit (ALU). However, the arithmetic and logic unit cannot perform binary subtractions directly. It performs binary subtractions using a process known asFor multiplication and division, the arithmetic and logic unit uses a method called shifting before adding the bits.

Representation of signed binary numbers

• In computer technology, there are three common ways of representing a signed binary number.

1. Prefixing an extra sign bit to a binary number.
2. Using ones compliment.
3. Using twos compliment.

Prefixing an extra sign bit to a binary number

• In decimal numbers, a signed number has a prefix “+” for a positive number e.g. +27₁₀ and “-“ for a negative number e.g.^-27
• However, in binary, a negative number may be represented by prefixing a digit 1 to the number while a positive number may be represented by prefixing a digit 0. For example, the 7-bit binary equivalent of 127 is 1111111₂. To indicate that it is positive, we add an extra bit (0) to the left of the number i.e. (0)1111111₂.
• To indicate that it is negative number we add an extra bit (1) i.e. (1)1111111₂.
• The problem of using this method is that the zero can be represented in two ways i.e.(0)0000000₂ and (1)0000000₂.

Binary Addition

It is a key for binary subtraction, multiplication, division. There are four rules of binary addition.

In fourth case, a binary addition is creating a sum of (1 + 1 = 10) i.e. 0 is written in the given column and a carry of 1 over to the next column.

Example − Addition

Binary Subtraction

Subtraction and Borrow, these two words will be used very frequently for the binary subtraction. There are four rules of binary subtraction.

Example − Subtraction

Binary Multiplication

Binary multiplication is similar to decimal multiplication. It is simpler than decimal multiplication because only 0s and 1s are involved. There are four rules of binary multiplication.

Example − Multiplication

Binary Division

Binary division is similar to decimal division. It is called as the long division procedure.

Example − Division