How to Solve Subtraction Problems Using 2's Complement
Would you like to know more about 2 's complement subtraction for kids? Well, then, you've come to the right place! This article will cover a 2's complement and how it works in subtraction with complements. Two binary numbers can be subtracted using the approach of the second complement. By the end of this article, you should be more confident with your ability to perform 2 's complement subtraction, including binary subtraction using 2's complement. Let's get started!
What is a 2 's Complement?
To implement this method for subtracting two binary numbers, the first step is to find the 2’s complement of the number to be subtracted from another number. To get the 2’s complement, first of all, 1’s complement is found, and then 1 is added. The addition is the required 2’s complement.
Suppose we need to find the 2’s complement of the binary number 10010. First, find 1’s complement. To find this, replace all 1 to 0 and all 0 to 1. Therefore, 1’s complement of 10010 will be 01101. Add 1 to this, and we will get the 2’s complement, i.e. 01110.
Binary Subtraction Using 2's Complement
To learn how to subtract binary numbers using 2's complement, which is the subtraction of a smaller number from a larger number using 2’s complement subtraction, the following steps are to be followed:
Step 1: Determine the 2’s complement of the smaller number
Step 2: Add this to the larger number.
Step 3: Omit the carry. Note that there is always a carry in this case.
The following example illustrates the above-mentioned steps:
Exampe: Subtract $(1010)_2$ from $(1111)_2$ using 2's complement method.
Ans:
Step 1: 2's complement of $(1010)_2$ is $(0110)_2$.
Step 2: Add $(0110)_2$ to $(1111)_2$.
This is shown below:
Subtract Using 2's Complement Method
To subtract a larger number from a smaller number using 2’s complement subtraction, the following steps are to be followed:
Step 1: Determine the 2’s complement of the smaller number.
Step 2: Add this to the larger number.
Step 3: There is no carry in this case. The result is in 2’s complement form and is negative.
Step 4: To get an answer in true form, take 2’s complement and change its sign.
Example: Subtract $(1010)_2$ from $(1000)_2$ using 2's complement.
Ans:
Step 1: Find the 2's complement of $(1010)_2$. It is $(0110)_2$.
Step 2: Add $(0110)_2$ to $(1000)_2$.
2’s complement
Step 3 and Step 4 have been explained in the above difference calculation.
Subtraction Using r's Complement:
Let's say you want to subtract the number 01010100 from 11100011. We can do this using 2 's complement by simply doing the subtraction using r's complement.
Steps to Find r's Complement:
To find r's complement, add 1 to the calculated ($r-1$) 's complement.
Here is an example:
Q. Find the 7's and 8's complement of the number $(5 63)_8$
Step 1: Identify the base (or) radix. Here $r=8$.
Step 2: Since 7 is the largest digit in the number system, subtract each digit of the given number from 7, i.e. if it's a three-digit number, subtract the number from 777.
$\therefore(214)_8$ is the 7's complement of a given number
Step 3: To find r's complement, i.e. 8's complement, then add ' 1 ' to the result of 7 's complement number.
$\therefore(215)_8$ is the 8 's complement of the given number.
Solved Examples
Q 1. 10110 - 11010
Ans: 11010 has a 2s complement of (00101+1) or 00110.
Add the 2's complement to the minuend (10110+00110) or 11100.
Now taking its complement;
The solution is (00011+1)= - (00100)
Q 2. 10110-01111
Ans: 01111's 2s complement is 10001.
The minuend plus the complement of two (10110-10001) equals 100111.
The response is 00111.
Q 3. 0100-11101
Ans: 11101's 2s complement is 00011
The minuend plus the complement of two (10100- 00011) equals 10111.
Since there is no carry here, the response is 01001.
Q 4. 110101 - 101001
Ans: 101001's complement in 2 is 010111
(110101-010111) Add the minuend and the 2's complement to get 1001100.
Carry, the result's leftmost bit is a 1 and is ignored.
The response is 001100.
Practice Questions
Q 1. 1001 - 0100
Ans: 0101
Q 2. 0100 - 1011
Ans: 1011
Q 3. 0110 - 0100
Ans: 0010
Q 4. 10110- 11101
Ans: 00111
Q 5. 110-101
Ans: 001
Summary
In conclusion, in this article, we went over two's complement subtraction. We've done an example problem to show you how it works and how it is performed on paper. The examples provided in this article are used for demonstration purposes only and thus do not necessarily model the types of problems you would encounter on a standardised test.
Instead of simply memorising the steps in this article, you should practice the problems. You can choose to use paper and pencil or use a calculator, 2 's complement subtraction calculator, or your fingers on your smartphone. Therefore, if you want to perform division (and thus subtraction) without using r's complement, you will need to learn how to use 2 's complement while performing division.
FAQs on 2's Complement Subtraction Made Easy
1. How do you subtract one's complement and two's complement?
To subtract numbers using one's complement, first find the one's complement (invert all bits) of the subtrahend and add it to the minuend. If there is a carry, add it back to the sum. In two's complement subtraction, take the two's complement of the subtrahend (invert all bits and add 1), then add it to the minuend. Ignore any carry out. These binary subtraction techniques simplify digital computations and help students understand binary arithmetic. Vedantu’s expert tutors often guide learners through these steps using interactive sessions and real-world examples.
2. How do you subtract 75 from 26 using 2's complement?
To subtract 75 from 26 using two's complement:
- Convert 26 and 75 to 8-bit binaries: $26 = 00011010$, $75 = 01001011$
- Find the two's complement of 75: invert bits ($10110100$) and add 1 ($10110100 + 1 = 10110101$)
- Add to 26: $00011010 + 10110101 = 11001111$
3. How do you subtract 36 from 83 using two's complement?
To subtract 36 from 83 using two's complement:
- Convert the numbers to 8-bit binary: $83 = 01010011$, $36 = 00100100$
- Find the two's complement of 36: invert ($11011011$), then add 1 ($11011011 + 1 = 11011100$)
- Add to 83: $01010011 + 11011100 = 100101111$
4. What is the 2s complement equal to?
The 2’s complement of a binary number is equal to its negative representation in binary arithmetic. To find the two’s complement, invert all the bits (perform the one's complement) and add 1. For example, the two’s complement of $00000101$ (5 in decimal) is $11111011$ (which is $-5$ in two’s complement representation for 8 bits). Vedantu’s academic support helps students practice and apply two’s complement concepts in both theoretical and practical contexts in computer science.
5. What are the advantages of using 2's complement subtraction in digital systems?
2's complement subtraction streamlines binary arithmetic as:
- There’s no need for dedicated subtraction circuits; addition can handle both positive and negative numbers.
- It simplifies hardware design for computers and calculators.
- It eliminates ambiguity around representing zero and negative numbers.
6. What are the steps to solve binary subtraction using two's complement method?
To perform binary subtraction using the two’s complement method, follow these steps:
- Convert both numbers to binary, ensuring equal bit lengths.
- Find the two's complement of the subtrahend (invert all bits and add 1).
- Add the result to the minuend’s binary value.
- Ignore any carry out of the most significant bit.
- If the result’s sign bit is 1, it’s negative. Convert back to decimal as needed.
7. How does 2's complement subtraction differ from other binary subtraction methods?
2's complement subtraction uses only addition (with two’s complement for negatives), whereas methods like borrow-and-subtract involve more manual bit manipulation. 2's complement is more efficient for digital logic and programming as:
- It uniformly represents both positive and negative values.
- There’s no need to handle the negative sign separately.
8. Why is overflow detection important in 2's complement subtraction?
Overflow in two’s complement subtraction occurs when the result exceeds the representable range for the chosen bit length. Detecting overflow ensures calculation accuracy and prevents computational errors. In binary subtraction, overflow can be checked by analyzing the sign bits of the operands and the result. Vedantu provides targeted exercises to help students recognize and prevent overflow while performing binary arithmetic.
9. What are practical applications of 2's complement subtraction in computer science?
2's complement subtraction is widely used in:
- Arithmetic logic units (ALUs) for performing calculations in computers.
- Programming languages to manage signed integer operations.
- Digital circuit design and microcontroller development.
