Half Adder and Full Adder Working

Half Adder and Full Adder  Working

Introduction:- Any electrical or electronic system can represent two states very reliably that is either on or off state. for example a light is on is one state and light is off is second state.There is no confusion about state. These can be state in binary number that is 1 or 0. Similarly in digital electronics  5 volt supply is used. If at any point voltage is 5 volt we say state is 1. If voltage is 0 volt we say state is 0.  To represent numbers in binary system we use set of 4 bit known as nibble. if we use 8 bits then it is known as byte.

if we want to use 4 bit we have to keep four place to store these bits. These places are called as registers. These registers are 4, 8 or 16 bit size. To shift value of one register to another register we need four (8 or 16) lines  known as data bus. To process the number we use airthematic logic unit in any digital computer system.

Basic of binary number addition:- For example if we want to add 6 and 7 in decimal system answer is 13. But in binary system number 6 is written as 0110 and number 7 is written as 0101.
we can add just like decimal system as given below

      11  carry
      0110         number 1    6
 ÷   0111         number 2    7
=    1101
=    13

In this binary addition we first add unit digit bit that is 0 and 1 sum = 1. Then second digit bit 1 ÷ 1 =10  there fore second digit ans is 0 and 1 as  carry for third digit. Now for third digit 1 ÷ 1= 10, again  add carry 1 from second digit so 10 ÷ 1 = 11. So ans for third digit is 1 and carry for forth digit is 1. In forth digit 0 ÷ 0= 0 now adding carry 0 ÷ 1= 1. So ans for forth digit is 1. So four digit ans is 1101 equal to 13 in decimal. Now see in digital system how these 0 and 1 are added in the same way shown above. We will consider only one bit addiyion with ExOo gate. The two bits to be added are connected to input of gate and output is taken as sum.

 Truth table of  ExOr gate
      b1      b2    sum
      0    +   0      0
      0    ÷   1      1
      1    ÷   0      1
      1.   ÷   1      0

So with this we get sum of first digit at  out put of ExOr  gate. To find carry bit we use one and gate with ExOr gate when both bits are 1 the output a of  AND gate become 1 which is used as carry bit for next bit addition.

The diagram of half adder is shown below.

Full Adder diagram

Here we can add two bit and carry bit from previous bit addition. The result is also sum bit and a carry bit for next stage.

Four bit adder diagram

                                                                                                                                                                                           

The addition of four bit make is used  for addition of binary numbers.The Full  adder is the basis of all digital computer ALU.

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