# Binary addition rules 1+1+1

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. Learn about electronics Digital Electronics. The largest positive value is characterized by the sign high-order bit being off 0 and all other bits being on 1. The smallest negative value is characterized by the sign bit being 1, and all other bits being 0.

Adding two values is straightforward. Simply align the values on the least significant bit and add, propagating any carry to the bit one position left. If the carry extends past the end of the word it is said to have "wrapped around", a condition called an " end-around carry ".

When this occurs, the bit must be added back in at the right-most bit. This phenomenon does not occur in two's complement arithmetic. Subtraction is similar, except that borrows, rather than carries, are propagated to the left.

If the borrow extends past the end of the word it is said to have "wrapped around", a condition called an " end-around borrow ".

When this occurs, the bit must be subtracted from the right-most bit. It is easy to demonstrate that the bit complement of a positive value is the negative magnitude of the positive value. Negative zero is the condition where all bits in a signed word are 1. This follows the ones' complement rules that a value is negative when the left-most bit is 1, and that a negative number is the bit complement of the number's magnitude. The value also behaves as zero when computing. Negative zero is easily produced in a 1's complement adder.

Simply add the positive and negative of the same magnitude. Although the math always produces the correct results, a side effect of negative zero is that software must test for negative zero.

The generation of negative zero becomes a non-issue if addition is achieved with a complementing subtractor. The first operand is passed to the subtract unmodified, the second operand is complemented, and the subtraction generates the correct result, avoiding negative zero. If the second operand is negative zero it is inverted and the original value of the first operand is the result.