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                  NPP               Number System, Boolean Algebra and Logic Circuits              301


                                                Truth Table: 2-input XOR gate
                                                  A A A      B B B    Y Y
                                                                      Y=A B⊕=A B⊕=A B⊕
                                                  0 0 0      0 0 0       0 0 0
                                                  0 0 0      1 1 1       1 1 1

                                                  1 1 1      0 0 0       1 1 1
                                                  1 1 1      1 1 1       0 0 0

                      Symbol: 2-input XOR gate                    2-BZnwQ> XOR H$m g§Ho$V

                                          A

                                          B                           Y = A + B

                      The Boolean expression for the output of    XOR JoQ> Ho$ AmCQ>nwQ> H$m ì`§OH$ Bg àH$ma h¡ …
                  XOR gate is:
                                                     Y  =  A    .B  +  A. B
                      Therefore we can write that                  Bgr{bE h_ H$h gH$Vo h¢ {H$

                                                     A⊕     A     B =  .B  +   A. B
                      Looking to the Truth Table of 2-input XOR   Cnamoº$ gË`-Vm{bH$m H$mo XoIZo na `h ñnîQ> hmoVm
                  gate it is clear that XOR gate gives Zero at the  h¡ {H$ `{X A = B h¡ Vmo AmCQ>nwQ> 0 hmoJm AÝ`Wm AmCQ>nwQ>
                  output when A=B and the output is one when A
                  is not equal to B. Therefore this property of 2-  1 hmoJm (A ≠ B ). Bgr{bE XOR JoQ> Xmo {~Q>m| H$s VwbZm
                  input XOR gate can be used to compare two bits.  H$aZo H$m H$m`© H$aVm h¡Ÿ& Bgo H$ånoaoQ>a Zm_H$ n[anW _|
                  Thus, XOR gate is used in comparator circuits  Cn`moJ H$aVo h¢, Omo Xmo ~mBZar g§»`mAm| H$s VwbZm H$a
                  which are used to compare two Binary numbers.  gH$Vm h¡Ÿ&
                       Another property of XOR gate is clear from  Bgr Vah gË`-Vm{bH$m go `h ^r ñnîQ> h¡ {H$ EH$
                  the  truth  table:  The output  of  XOR gate is  XOR JoQ> Xmo {~Q>m| H$m A§H$ J{UVr` `moJ àXmZ H$aVm h¡Ÿ&
                  arithmetic sum of all the input bits. Therefore  Bgr{bE BgH$m Cn`moJ H$åß`yQ>a Ho$ Eogo n[anWm| _| {H$`m
                  XOR gate is used in Adder circuits which are  OmVm h¡ Omo Xmo ~mBZar g§»`mAm| H$mo Omo‹S>Zo H$m H$m`© H$aVo
                  used to add two binary numbers. Interestingly  h¢Ÿ& Eogo n[anWm| H$mo ~mBZar EoS>a H$hVo h¢Ÿ& gmW hr BgH$m
                  the XOR gate output gives difference of two bits.  Cn`moJ Xmo {~Q>m| H$mo KQ>mZo Ho$ {bE ^r {H$`m OmVm h¡Ÿ& Eogo
                  Therefore it is also used in subtractor circuit.  n[anW H$mo g~Q´>oŠQ>a H$hVo h¢Ÿ&
                      The XOR gate can also be used as a parity   XOR JoQ> H$m Cn`moJ no[aQ>r H$mo Om±MZo Ho$ {bE ^r
                  checker. Give the binary number at the inputs  {H$`m OmVm h¡Ÿ& Š`m|{H$ BZnwQ> na `{X 1 H$s g§»`m {df_
                  of the  XOR gate. The  output  is one  for  odd
                  number of ones and is Zero for even number of  h¡ Vmo AmCQ>nwQ> 1 hmoJm AÝ`Wm AmCQ>nwQ> eyÝ` hmoJmŸ&
                  ones.  XOR  gate  can also be used in  parity  BgH$m Cn`moJ no[aQ>r MoH$a d no[aQ>r OZaoQ>a Zm_H$ n[anWm|
                  generators.                                 _| hmoVm h¡Ÿ&
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