# Binary addition and subtraction rules

The Web This site. Arithmetic rules for binary numbers are quite straightforward, and similar to those used in decimal arithmetic. The rules for addition of binary numbers are:. Notice that in Fig. Binary addition is carried out just like decimal, by adding up the columns, starting at the right and working column by column towards the left.

For example, in Fig. The rules for subtraction of binary numbers are again similar to decimal. The subtraction rules for binary are quite simple even if the borrow and pay back system create some difficulty. The rules for binary subtraction are quite straightforward except that when 1 is subtracted from 0, a borrow must be created from the next most significant column.

This borrow is then worth 2 10 or 10 2 because a 1 bit in the next column to the left is always worth twice the value of the column on its right. Notice that in the third column from the right 2 2 a borrow from the 2 3 column is made and then paid back in the MSB 2 3 column. Borrowing 1 from the next highest value column to the left converts the 0 in the 2 2 column into 1 0 2 and paying back 1 from the 2 2 column to the 2 3 adds 1 to that column converting the 0 to 0 1 2.

Once these basic ideas are understood, binary subtraction is not difficult, but does require some care. As the main concern in this module is with electronic methods of performing arithmetic however, it will not be necessary to carry out manual subtraction of binary numbers using this method very often. This is because electronic methods of subtraction do not use borrow and pay back, as it leads to over complex circuits and slower operation.

Computers therefore, use methods that do not involve borrow. These binary addition and subtraction rules will be fully explained in Number Systems Modules 1. Just to make sure you understand basic binary subtractions try the examples below on paper. Be sure to show your working, including borrows and paybacks where appropriate. Using the squared paper helps prevent errors by keeping your binary columns in line.

This way you will learn about the number systems, not just binary addition and subtraction rules numbers. This is not a problem with this example as the answer 2 10 10 still fits within 4 bits, but what would happen if binary addition and subtraction rules total was greater than 15 10?

As shown in Fig 1. When arithmetic is carried out by electronic circuits, storage locations called registers are binary addition and subtraction rules that can hold only a definite number of bits.

If the register can only hold four bits, then this **binary addition and subtraction rules** would raise a problem. The final carry bit is lost because it cannot be accommodated in the 4-bit register, therefore the answer will be wrong.

To handle larger numbers more bits must be used, but no matter binary addition and subtraction rules many bits are used, sooner or later there must be a limit. Hons All rights reserved. Learn about electronics Digital Electronics. After studying this section, you should be able to: Understand the rules used in binary calculations. Understand limitations in binary arithmetic.