Binary Addition using 2’s Complement
When negative numbers are expressed in binary addition using 2’s complement the addition of binary numbers becomes easier. This operation is almost similar to that in 1’s complement system and is explained with examples given below:
A. Addition of a positive number and a negative number.
We consider the following cases.
Case I: When the positive number has a greater magnitude
In this case the carry which will be generated is discarded and the final result is the result of addition.
The following examples will illustrate this method in binary addition using 2’s complement:
In a 5-bit register find the sum of the following by using 2’s complement:
(i) -1011 and -0101
Solution:
+ 1 0 1 1 ⇒ 0 1 0 1 1- 0 1 0 1 ⇒ 1 1 0 1 1 (2’s complement)
(Carry 1 discarded) 0 0 1 1 0
Hence the sum is + 0110.
(ii) + 0111 and – 0011.
Solution:
+ 0 1 1 1 ⇒ 0 0 1 1 1- 0 0 1 1 ⇒ 1 1 1 0 1
(Carry 1 discarded) 0 0 1 0 0
Hence the sum is + 0100.
Case II: When the negative number is greater.
When the negative numbers is greater no carry will be generated in the sign bit. The result of addition will be negative and the final result is obtained by taking 2’s complement of the magnitude bits of the result.
The following examples will illustrate this method in binary addition using 2’s complement:
In a 5-bit register find the sum of the following by using 2’s complement:
(i) + 0 0 1 1 and - 0 1 0 1
Solution:
+ 0 0 1 1 ⇒ 0 0 0 1 1- 0 1 0 1 ⇒ 1 1 0 1 1 (2’s complement)
1 1 1 1 0
2’s complement of 1110 is (0001 + 0001) or 0010.
Hence the required sum is - 0010.
(ii) + 0 1 0 0 and - 0 1 1 1
Solution:
+ 0 1 0 0 ⇒ 0 0 1 0 0- 0 1 1 1 ⇒ 1 1 0 0 1 (2’s complement)
1 1 1 0 1
2’s complement of 1101 is 0011.
Hence the required sum is – 0011.
B. When the numbers are negative.
When two negative numbers are added a carry will be generated from the sign bit which will be discarded. 2’s complement of the magnitude bits of the operation will be the final sum.
The following examples will illustrate this method in binary addition using 2’s complement:
In a 5-bit register find the sum of the following by using 2’s complement:
(i) – 0011 and – 0101
Solution:
- 0 0 1 1 ⇒ 1 1 1 0 1 (2’s complement)
- 0 1 0 1 ⇒ 1 1 0 1 1 (2’s complement)
(Carry 1 discarded) 1 1 0 0 0
2’s complement of 1000 is (0111 + 0001) or 1000.
Hence the required sum is – 1000.
(ii) -0111 and – 0010.
Solution:
- 0 1 1 1 ⇒ 1 1 0 0 1 (2’s complement)- 0 0 1 0 ⇒ 1 1 1 1 0 (2’s complement)
(Carry 1 discarded) 1 0 1 1 1
2’s complement of 0111 is 1001.
Hence the required sum is – 1001.
- Decimal Number System
- Why Binary Numbers are Used
- Binary to Decimal Conversion
- Conversion of Numbers
- Hexa-decimal Number System
- Conversion of Binary Numbers to Octal or Hexa-decimal Numbers
- Octal and Hexa-Decimal Numbers
- Signed-magnitude Representation
- Radix Complement
- Diminished Radix Complement
- Arithmetic Operations of Binary Numbers
From Binary Addition using 2’s Complement to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Adding 1-Digit Number | Understand the Concept one Digit Number
Sep 17, 24 02:25 AM
Understand the concept of adding 1-digit number with the help of objects as well as numbers. -
Counting Before, After and Between Numbers up to 10 | Number Counting
Sep 17, 24 01:47 AM
Counting before, after and between numbers up to 10 improves the child’s counting skills. -
Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern
Sep 17, 24 12:10 AM
Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures… -
Arranging Numbers | Ascending Order | Descending Order |Compare Digits
Sep 16, 24 11:24 PM
We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma… -
Worksheet on Tens and Ones | Math Place Value |Tens and Ones Questions
Sep 16, 24 02:40 PM
In math place value the worksheet on tens and ones questions are given below so that students can do enough practice which will help the kids to learn further numbers.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.