# Binary addition and subtraction rules

These methods 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 the 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 the total was greater than 15 10?

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

If the register can only hold four bits, then this example 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 how 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. 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 methods 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 the 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 the total was greater than 15 10?

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

If the register can only hold four bits, then this example 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 how many bits are used, sooner or later there must be a limit.

Hons All rights reserved.