• Skip to main content
  • Skip to primary sidebar
  • Skip to secondary sidebar
  • Skip to footer

Computer Notes

Library
    • Computer Fundamental
    • Computer Memory
    • DBMS Tutorial
    • Operating System
    • Computer Networking
    • C Programming
    • C++ Programming
    • Java Programming
    • C# Programming
    • SQL Tutorial
    • Management Tutorial
    • Computer Graphics
    • Compiler Design
    • Style Sheet
    • JavaScript Tutorial
    • Html Tutorial
    • Wordpress Tutorial
    • Python Tutorial
    • PHP Tutorial
    • JSP Tutorial
    • AngularJS Tutorial
    • Data Structures
    • E Commerce Tutorial
    • Visual Basic
    • Structs2 Tutorial
    • Digital Electronics
    • Internet Terms
    • Servlet Tutorial
    • Software Engineering
    • Interviews Questions
    • Basic Terms
    • Troubleshooting
Menu

Header Right

Home » C » Variables » Storage of Signed Integers
Next →
← Prev

Storage of Signed Integers

By Dinesh Thakur

To store signed integers, we need to reserve one bit for the sign of the integer. It is usual convention to use a 0 bit to indicate positive sign and a 1 bit to indicate a negative sign.

Taking the bit numbering as [B2 B1 B0] and reserving the leftmost bit for the sign, we can associate a value of N with each pattern as

N = (-1)B2 * (B1 * 21 + B0 * 20)

This results in the following values for each of the 8 bit patterns.

000

001

010

011

100

101

110

111

+0

+1

+2

+3

-0

-1

-2

-3

This simplistic scheme (known as “sign + magnitude” scheme) has two main problems. First, there are two zeros, i.e., a +0 and a -0. Second, we get only 7 integers being represented by 8 binary patterns because of the wasted pattern for the -0. The 2s-complement scheme solves this problem. Let us see how negative integers are stored in the 2s-complement scheme. If we have to store -2 in 3 bits, we first find the binary pattern for +2.

binary pattern for +2     010

next we take its ls-complement by changing all ls to 0s and all 0s to 1s (i.e., flipping or toggling all its bits).

Taking ls-complement 101

The last step is to add 1

Adding 1 to 101, we get 110

The complete listing is shown in Table for 3 bits and in Next Table for 4 bits.

             Table Signed 3-bit Integer Representation (2s-cornplernent)

000

001

010

011

100

101

110

111

0

1

2

3

-4

-3

-2

-1

We have represented the unsigned integers from -4 (= -22) to 3 (=22-1) using three bits. By extending this scheme to K bits, we see that we can store unsigned integers from a minimum of (-2K-1) to a maximum of (2 K-1 – 1). The 16 signed numbers possible for a 4 bit representation are shown in Table

    Table Signed 4-bit Integer Representation (2s-cornplernent)

Binary

Decimal

Binary

Decimal

0000

0

1000

-8

0001

1

1001

-7

0010

2

1010

-6

0011

3

1011

-5

0100

4

1100

-4

0101

5

1101

-3

0110

6

1110

-2

0111

7

1111

-1

Let us revise what we have learnt taking a one byte representation of an integer as an example. If we need to store only unsigned integers, then it is possible to store integers ranging from 0 (corresponding to the binary value 00000000 and it’s equivalent hexadecimal value of 00) to 255 (corresponding to the binary value 11111111 and it’s equivalent hexadecimal value of FF). Therefore, there are 256 different integers which can be stored in this one byte unsigned integer representation which correspond to the 256 different bit patterns that can be generated using 8 bits (256 = 28).

But, if we want to store signed integers, the maximum positive integer that can be represented using 7 bits is 127 (corresponding to the binary value 01111111 and its equivalent hexadecimal value of 7F). The negative integers are stored using a 2’s complement representation and the minimum negative integer works out to be -128 (corresponding to the binary value 10000000 and its equivalent hexadecimal value of 80). The correspondence of the various bit patterns with the unsigned and signed integers is represented in Table.

Notice the unusual correspondence between the signed and the unsigned integers. The unsigned integer 128 corresponds to the signed integer value of -128 and the unsigned integer 255 corresponds to the signed integer value of -1.

You’ll also like:

  1. Write a C program to read and output Signed octal.
  2. What is a Storage class
  3. C storage class Specifiers
  4. C program to find the array of integers contain a duplicate number
  5. C Program for GCD of Two Integers using Euclid’s algorithm
Next →
← Prev
Like/Subscribe us for latest updates     

About Dinesh Thakur
Dinesh ThakurDinesh Thakur holds an B.C.A, MCDBA, MCSD certifications. Dinesh authors the hugely popular Computer Notes blog. Where he writes how-to guides around Computer fundamental , computer software, Computer programming, and web apps.

Dinesh Thakur is a Freelance Writer who helps different clients from all over the globe. Dinesh has written over 500+ blogs, 30+ eBooks, and 10000+ Posts for all types of clients.


For any type of query or something that you think is missing, please feel free to Contact us.


Primary Sidebar

C Programming

C Programming Tutorials

  • C - History
  • C - Anatomy
  • C - Constants
  • C - Identifiers
  • C - Data Types
  • C - Libraries File
  • C - Header Files
  • C - Basic Language
  • C - Data Types Sizes
  • C - Header Files Importance
  • C - Escape Sequences
  • C - Main() Purpose
  • C - Program Procedure
  • C - Control Statements
  • C - Enumeration Constant
  • C - Add numbers
  • C - Return Statement
  • C - Avoid Goto
  • C - Command Line Arguments
  • C - Switch Case
  • C - Switch Case Limitations
  • C - getchar() and putchar()
  • C - Iteration Statements
  • C - Pass by Value and Reference
  • C - Structures and Unions
  • C - Structure
  • C - Dynamic Memory
  • C - Fgets and Fputs Functions
  • C - Gets() and Puts() Functions
  • C - Armstrong Number
  • C - Storage Classes
  • C - Fibonacci Series
  • C - Precision Setting
  • C - const Parameters

C - Variable & It's Type

  • C - Variables
  • C - Variable Lifetime
  • C - Static Variable
  • C - Register Variable
  • C - Global Variables
  • C - Auto Variables
  • C - Local Variables

C - Operator & Expressions

  • C - Operator
  • C - Boolean Operators
  • C - Bitwise Operator
  • C - Arithmetic Operators
  • C - Modulus Operator
  • C - Ternary Operator
  • C - Expressions
  • C - Arithmetic Expressions

C - Array

  • C - Arrays
  • C - Array Types
  • C - Array Characteristics
  • C - Static Arrays
  • C - Global Arrays
  • C - 3D Arrays
  • C - Dynamic Arrays
  • C - Pointer to 3D Arrays
  • C - Array Elements Hold
  • C - Arrays as Function Parameters
  • C - Accessing Matrix Elements
  • C - File Handling
  • C - Matrix Multiplication
  • C - Dynamic Memory Allocation

C - Searching & Sorting

  • C - Data Structures
  • C - Linear Search
  • C - Bubble Sort
  • C - Merge Sort
  • C - Linked List
  • C - Insertion Sort
  • C - Binary Search
  • C - Selection Sort
  • C - Quick Sort

C - Functions

  • C - Functions
  • C - Functions Advantages
  • C - Void Functions
  • C - Function Call
  • C - Default Return Value
  • C - String functions

C - Pointer

  • C - Pointers
  • C - Type Casting Of Pointers
  • C - Pointer Advantages
  • C - Pointers Initialization
  • C - Vectors and Pointers

C - Differences

  • C - C Vs C++
  • C - Formal Args. Vs Actual Args.
  • C - Keywords Vs Identifiers
  • C - Strings Vs Character Arrays
  • C - Address Vs Dereference Operator
  • C - Goto Vs longjmp
  • C - Declaring Vs Defining Variable
  • C - String Vs Array
  • C - Call by Value Vs Reference
  • C - Structure Vs Union
  • C - For Vs While loops
  • C - Compiler Vs Interpreter

C - Programs

  • C Program Standard Deviation
  • C Program Calculate Tax
  • C Program Sum Series
  • C Program Merge Arrays
  • C Program Euclid’s Algorithm
  • C Program Print Weekdays
  • C Program Sum of Digits
  • C Program Print a list
  • C Program Print Pythagorean
  • C Program Quiz program
  • C Program Display Table
  • C Program Print Comma-Separated
  • C Program Prints Prime Numbers
  • C Program for Print Integer
  • C Program Count Number
  • C Program Print Color Name
  • C Program Print Odd Numbers
  • C Program Calculate area
  • C Program for a Menu
  • C Program Add Two Vectors
  • C Program Array Addresses
  • C Program Division by Zero Error
  • C Program Compare two Dates
  • C Program Tower of Hanoi
  • C Program return 3 Numbers
  • C Program for Prime Numbers
  • C Program for Factorial
  • C Program for Palindrome

Other Links

  • C Programming - PDF Version

Footer

Basic Course

  • Computer Fundamental
  • Computer Networking
  • Operating System
  • Database System
  • Computer Graphics
  • Management System
  • Software Engineering
  • Digital Electronics
  • Electronic Commerce
  • Compiler Design
  • Troubleshooting

Programming

  • Java Programming
  • Structured Query (SQL)
  • C Programming
  • C++ Programming
  • Visual Basic
  • Data Structures
  • Struts 2
  • Java Servlet
  • C# Programming
  • Basic Terms
  • Interviews

World Wide Web

  • Internet
  • Java Script
  • HTML Language
  • Cascading Style Sheet
  • Java Server Pages
  • Wordpress
  • PHP
  • Python Tutorial
  • AngularJS
  • Troubleshooting

 About Us |  Contact Us |  FAQ

Dinesh Thakur is a Technology Columinist and founder of Computer Notes.

Copyright © 2025. All Rights Reserved.

APPLY FOR ONLINE JOB IN BIGGEST CRYPTO COMPANIES
APPLY NOW