NIMCET Complements Notes: Number Representation, 1's and 2's Complement
Mishika Gupta9 Oct, 2026
Understanding binary number representation can be challenging when different methods are used to represent positive and negative numbers. Concepts such as sign-magnitude, 1's complement and 2's complement follow different rules. Signed and unsigned integers, bit patterns and binary calculations also form part of Computer Awareness, making it important to understand how each representation works.
These NIMCET Complements Notes explain the key concepts with clear definitions, rules, tables and worked examples. They cover number representation, sign-magnitude, 1's complement, 2's complement, signed and unsigned integers, and the differences between these methods to support focused revision for NIMCET Computer Awareness.
What Are Complements in Number System?
Complements are methods used in computer systems to represent and process numbers, particularly negative integers. They are closely related to binary number representation and are important for performing arithmetic operations within a computer.
The main representations of integers covered in this topic are:
-
Sign-Magnitude
-
1's Complement
-
2's Complement
Representation of Numbers in Computers
A computer needs to represent different types of information, including positive integers, negative integers, fractions, real numbers and characters.
For integer representation, the commonly studied methods include Sign-Magnitude, 1's Complement and 2's Complement.
|
Representation |
Main Concept |
|
Sign-Magnitude |
MSB represents the sign, and the remaining bits represent the magnitude |
|
1's Complement |
Every 0 is changed to 1, and every 1 is changed to 0 |
|
2's Complement |
Find the 1's complement and add 1 |
These concepts are part of the broader number-system topics tested in Computer Awareness. The NIMCET preparation resources cover other areas that can be studied alongside number-system concepts.
Sign-Magnitude Representation
In Sign-Magnitude representation, the Most Significant Bit (MSB) represents the sign of the number.
|
Aspect |
Details |
|
Sign-Magnitude Rule |
In an n-bit number, 0 represents a positive number, and 1 represents a negative number. The remaining bits represent the magnitude. |
|
+13 |
13 in binary using 7 bits is 0001101. With 0 as the sign bit, the 8-bit representation is 00001101. |
|
-13 |
The sign bit becomes 1, giving the 8-bit representation 10001101. |
|
+13 Representation |
00001101 |
|
-13 Representation |
10001101 |
Unsigned and Signed Integers
The number of bits determines how many different values can be represented.
|
Aspect |
Details |
|
Total Values (8-bit) |
28=256 possible values |
|
Unsigned Integers |
Use all 8 bits to represent the value, without a separate sign bit. |
|
Unsigned Integer Range |
0 to 255 |
|
Signed Integers |
Represent both positive and negative numbers. The range depends on the representation method. |
|
Signed Integer Range (Sign-Magnitude or 1's Complement) |
-127 to +127 |
|
Signed Integer Range (2's Complement) |
-128 to +127 |
Disadvantage of Sign-Magnitude Representation
One important limitation of sign-magnitude representation is that it has two representations of zero.
|
Topic |
Original Number / Rule |
Calculation or Explanation |
Result |
|
Sign-Magnitude: Positive Zero |
+0 |
Sign bit = 0 |
00000000 |
|
Sign-Magnitude: Negative Zero |
-0 |
Sign bit = 1 |
10000000 |
|
Sign-Magnitude: Unsigned +22 |
+22 |
8-bit binary representation |
00010110 |
|
Sign-Magnitude: Signed +22 |
+22 |
Sign bit = 0 |
00010110 |
|
Sign-Magnitude: Signed -22 |
-22 |
Sign bit = 1 |
10010110 |
|
1's Complement Rule |
Any binary number |
Flip every bit: 0 → 1, 1 → 0 |
— |
|
1's Complement Example 1 |
10110010 |
Flip every bit |
01001101 |
|
1's Complement Example 2 |
101101 |
Flip every bit |
010010 |
|
1's Complement Example 3 |
101 |
Flip every bit |
010 |
|
2's Complement: Standard Method |
10110010 |
1's complement: 01001101; add 1 |
01001110 |
|
2's Complement: Fast Trick |
101101 |
From the right, copy bits through the first 1, then flip the remaining bits |
010011 |
|
2's Complement Example 1 |
101 |
1's complement: 010; add 1 |
011 |
|
2's Complement Example 2 |
101101 |
1's complement: 010010; add 1 |
010011 |
|
2's Complement Example 3 |
11100100100 |
1's complement: 00011011011; add 1 |
00011011100 |
|
2's Complement Example 4 |
100 |
3-bit representation; 1's complement: 011; add 1 |
100 |
Difference Between 1's Complement and 2's Complement
Understanding the difference between 1's complement and 2's complement helps clarify how each method converts binary numbers and represents negative integers.
|
Basis |
1's Complement |
2's Complement |
|
Basic operation |
Flip every bit |
Find 1's complement and add 1 |
|
Rule |
0 → 1, 1 → 0 |
1's complement + 1 |
|
Example for 101 |
010 |
011 |
|
Calculation |
Direct bit inversion |
Bit inversion followed by addition |
For additional NIMCET examination information and related preparation resources, the NIMCET exam resources cover the broader exam-related areas alongside topic-wise preparation.
NIMCET Complements Notes PDF
Keeping the key rules and examples together can make last-minute revision easier. The NIMCET Complements PDF covers number representation, sign-magnitude, 1's complement, 2's complement and worked examples.
NIMCET System Devices Notes PDF
For additional support with NIMCET preparation, the NIMCET batches include learning resources for revising Computer Awareness and other exam topics.
How to Prepare Complements for NIMCET?
A clear understanding of the rules can make binary complement questions easier to solve. Focus on the following points:
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Understand sign-magnitude: Know how the MSB represents the sign and how the remaining bits represent magnitude.
-
Practise 1's complement: Remember that every 0 changes to 1 and every 1 changes to 0.
-
Learn both 2's complement methods: Practise the standard method as well as the faster LSB technique.
-
Work with different bit lengths: Solve examples using 3-bit, 6-bit, 8-bit and other representations.
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Revise signed and unsigned ranges: These are useful for direct Computer Awareness questions.
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Solve MCQs: Practise questions involving binary conversion, complements and number representation.
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Revise regularly: Short revision sessions can help retain the rules and calculation steps.
For the upcoming examination cycle, NIMCET 2027 includes examination-related information and resources relevant to the 2027 preparation cycle.
Complements are an important part of binary number representation and can appear in NIMCET Computer Awareness questions. Focus on understanding sign-magnitude representation, the rules for finding 1's and 2's complements, signed and unsigned ranges, and the fast method for calculating 2's complement.
NIMCET Complements Notes FAQs
What are complements in computer number systems?
What is Sign-Magnitude representation?
How many values can be represented using 8 bits?
Why are 1's and 2's complements important for NIMCET?
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