By Anand George SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Binary Numbers  The numbers we use in our daily life are called 10 based numerals.  For example number 348 is equal to (3 x 100) + (4 x 10) + 8  While humans use 10 based numerals computers use 2 based numerals which as only 1 and 0 s in any number. SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Demo  10 based numerals and  2 based numeral in calc SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Some Mapping of 10 based Numerals and 2 based Numerals. 10 based number2 base equivalent SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Some jargons  One digit of 2 based numeral is called a ‘bit’.  8 bits gives a byte  2 bytes or 16 bits give a word.  4 bytes or 32 bit gives a dword or doubleword. SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Some facts  Any number can be expressed in 2 based numeral.  A 2 based number of n digits can hold a number which has max value 2^n - 1 ( 2 to power n ) – 1.  Everything you see or deal with in a computer – programs, video, music, your facebook page…. name it..all 1s and 0s…which is a 2 based number or collection of 2 based numbers.  What makes the difference is the way different programs interpret the binary number. For example your facebook page is a big binary number which is interpreted by your browser as a web page and display it as a web page. Same big binary number can be something else to some other program or piece of code. SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Digital Operations on 2 based numbers.  We do operations like addition, subtraction etc which decimal or 10 based numerals in a daily bases.  2 based numerals also has all those operations.  2 based numeral has some additional operations as well.  AND, NOT, OR, NOR, XOR, Left Shift, Right Shift etc. SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

AND operation Input operand 1Input operand 2AND Output SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

OR Input operand 1Input operand 2OR Output SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Exclusive OR ( ExOR ) Input operand 1Input operand 2ExOR Output SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

NOT or Ones complement ( unary operator as there is only one operand) Input operand 1NOT Output SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Shift operations  Left Shift  Right Shift OperationValue Initial0001 Left Shift by 1 bit0010 Left Shift by 1 bit0100 Left Shift by 1 bit1000 OperationValue Initial1100 Right Shift by 1 bit0110 Right Shift by 1 bit0011 Right Shift by 1 bit0001 SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Demo  Visual Studio  Bitwise operation In C.  OR |  AND &  NOT ^  Left Shift  Right Shift SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Operations ( cont )  These operations has some special physical means when it comes to 2 based numerals.  Few Examples 1. AND has properties of Multiplication. 2. OR has properties of Addition 3. Left shift is equal to Multiplication by 2 4. Right shift is equal to division by 2 SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Demo  Show bit program SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Hexadecimal Numbers.  Has 16 Digits 0-9 then A, B, C, D, E, F  No relation with computers.  Easy to map to binary numbers.  0xDEADBEAD is a hex decimal 32 bit number.  Conversion to binary is very easy as each just concatenate conversion of each digits.  So most of the display of binary numbers in computers are via hex decimal to save space and better readability. SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Example conversion to binary  0xDEADBEAD  0x1234ABCD SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Demo  In calc.exe conversion. SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

negative numbers  2’s compliment SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Demo of 2’s compliment SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Bit Fields struct myBits { bool first : 1; bool second : 1; bool third : 1; bool forth : 1; }; SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Demo  Bit Fields SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)

Thank you SourceLens.org Copyright. All rights reserved. Content Owner - Meera R (meera at sourcelens.org)