• Home
  • General Knowledge
    • Basic G. K.
    • World History
    • Indian History
    • Geography
    • Indian Constitution
    • Physics
    • Chemistry
    • Biology
    • Book & Author
    • Honour & Award
    • General Knowledge Test
  • General Aptitude
    • General Aptitude
    • Numerical Aptitude
    • Verbal Aptitude
    • Non- Verbal Aptitude
    • General Aptitude Test
  • Current Affairs
    • Current Day
    • Current Weak
    • Current Month
    • Current Year
  • Computer Tutorial
    • Basic Computer
    • Computer Fundamental
    • Computer Network
    • C- Tutorial
    • C- Programming
    • Linux Tutorial
    • Linux Commands
  • Objective MCQ
    • General Knowledge
    • Computer Engineering
    • General Aptitude
    • Verbal and Reasoning
    • Engineering
    • Medical Science
    • English
  • Introduction to Computer
  • Generation of Computer
  • Types of Computer
  • Component of Computer
  • Central Processing Unit
  • Input devices
  • Output devices
  • Computer Memory
  • Computer Ports
  • Computer Software
  • Programming Language
  • Flow Chart
  • Number System
  •   » Kinds of Number Systems
  •   » Converting Decimal Integer to Binary, Octal, Hexadecimal
  •   » Converting Decimal Fraction to Binary, Octal, Hexadecimal
  •   » Converting Decimal Integer Fraction to Binary, Octal, Hexadecimal
  •   » Conversion of Binary, Octal, Hexadecimal to Decimal
  •   » Conversion of Binary to Octal, Hexadecimal
  •   » Conversion of Octal, Hexadecimal to Binary
  •   » Binary Arithmetic
  •   » Complement of Binary Numbers
  •   » Binary Data Representation
  •   » Binary Coding Schemes
  • Operation System
  • DOS OS & Commands
  • Computer Network
  • Internet
  • MCQ on FOC

Complement of Binary Numbers


Home » Fundamental of Computer » Number System » Complement of Binary Numbers
« Previous
Next »

Complement of Binary Numbers

Complements are used in computer for the simplification of the subtraction operation. For any number in base r, there exist two complements—(1) r’s complement and (2) r-1 ’s complement.

Number System Base Complements possible
Binary 2 1’s complement and 2’s complement
Octal 8 7’s complement and 8’s complement
Decimal 10 9’s complement and 10’s complement
Hexadecimal 16 15’s complement and 16’s complement

Signed and Unsigned Numbers

A binary number may be positive or negative. Generally, we use the symbol “+” and “−” to represent positive and negative numbers, respectively. The sign of a binary number has to be represented using 0 and 1, in the computer. An n-bit signed binary number consists of two parts—sign bit and magnitude. The left most bit, also called the Most Significant Bit (MSB) is the sign bit. The remaining n-1 bits denote the magnitude of the number.

In signed binary numbers, the sign bit is 0 for a positive number and 1 for a negative number.
For example, 01100011 is a positive number since its sign bit is 0, and, 11001011 is a negative number since its sign bit is 1. An 8–bit signed number can represent data in the range −128 to +127 (–27to +27−1). The left-most bit is the sign bit.

Signed Numbers Representation

In an n-bit unsigned binary number, the magnitude of the number n is stored in n bits. An 8–bit unsigned number can represent data in the range 0 to 255 (28 = 256).

1’s Complement of Binary Number

1’s Complement of Binary Number is computed by changing the bits 1 to 0 and the bits 0 to 1
Example
» 1’s complement of 101 is 010
» 1’s complement of 1011 is 0100
» 1’s complement of 1101100 is 0010011

2’s Complement of Binary Number

2’s Complement of Binary Number is computed by adding 1 to the 1’s complement of the binary number.
Example
» 2’s complement of 101 is 010 + 1 = 011
» 2’s complement of 1011 is 0100 + 1 = 0101
» 2’s complement of 1101100 is 0010011 + 1 = 0010100

The rule to find the complement of any number N in base r having n digits is
(r − 1)’s complement — (rn − 1) − N
(r’s) complement —(rn − 1) − N + 1 = (rn − N)


« Previous
Next »

You may also like-

Converting Decimal Fraction to Binary, Octal, Hexadecimal Computer Hardware Touch Screen

General Information

GENERAL NOTE 2019 © All Right Reserved.