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Binary Subtraction


Binary subtraction is among the four binary operations, in which we use the subtraction method to differentiate between two binary values. Usually, this subtraction is between only two digits, 0 and 1. This procedure is analogous to simple arithmetic subtraction on decimal numbers in Math. As a result, when we subtract one from zero, we must borrow one from the next higher order digit to lower the digit by one, and the residual number left here is likewise 1.

Binary Operations are the crux of making the computer understand the way how mathematical operations are done. Because a computer can operate only under true or false, or 0 and 1, binary operations are important to make the computer comprehend the basics of math. The binary operations are very important for engineering students pursuing electronics and computer engineering.

Binary number subtraction is similar to a mathematical procedure comparable to decimal number subtraction or base 10 number subtraction. For example, in the decimal number system the addition of, 1 + 1 = 2 while in the binary number system, 1 + 1 = 10. When adding and subtracting binary integers, you must exercise caution while borrowing since this will occur more frequently.

When subtracting many columns of binary numbers, you must account for borrowing. When one is subtracted from zero, the result is one, with one borrowed from the next highest order bit or digit.

Let us look at some basic subtraction of binary numbers, which are important to advance further in this topic:

  • 0 – 0 = 0; the first subtraction is of 0 with 0, which, as we can see, yields 0.
  • 0 – 1 = 1, the second subtraction is between 0 and 1. This subtraction yields 1 in binary, while in the decimal system, this will give -1. Since 0 is smaller than 1, subtraction is done by borrowing from a higher digit.
  • The third subtraction is between 1 and 0, which simply gives 1 – 0 = 1
  • The final subtraction is between two binary digits of value 1, which, when subtracted with each other, gives 1 – 1 = 0.

These are also considered the fundamental rules of binary subtraction, and all the high-level subtraction is done keeping in mind these four rules.

1’s Complement

A number's 1's Complement is derived by reversing every 0 to 1 and every 1 to 0 in a binary integer. For example, binary integer 101 has a 1's Complement of 010. Please follow the instructions below to conduct binary subtraction using 1's Complement.

Step 1: Determine the subtrahend's 1's Complement. Subtrahend is known as the second number of subtractions in binary.

Step 2: Combine it with the minuend. The minuend is the first number of subtractions in binary.

Step 3: If there is a borrow, combine it with the result from step 2.

Step 4: If no borrow exists, the result of step 2 is the difference of the two integers using 1's complement binary subtraction.

This is an easy method for calculating the subtraction between two binary numbers and applied to computer programming for fast processing.

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