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Bộ cộng (Adder)

Thứ năm, 24 Tháng 6 2010 02:34 Quản trị viên

 

Adders are the basic building blocks of all arithmetic circuits; adders add two binary numbers and

give out sum and carry as output. Basically we have two types of adders.

Half Adder.

Full Adder.

Half Adder

 Adding two single-bit binary values X ! produces a sum " bit and a carry out #-out bit. $hisoperation is called half addition and the circuit to reali%e it is called a half adder.

  Truth Table

 

X Y SUM CARRY

& & & &

& ' ' &

' & ' &

' ' & '

  Symbol

  " (X!) * ('+)

  " * X,! X!,

  " * X !

  #A!(X!) * (/)

  #A! * X!

  Circuit

 

Full Adder

 Full adder takes a three-bits input. Adding two single-bit binary values X ! with a carry input bit

#-in produces a sum bit " and a carry out #-out bit.

  Truth Table

  X Y Z SUM CARRY

& & & & &

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& & ' ' &

& ' & ' &

& ' ' & '

' & & ' &

' & ' & '

' ' & & '

' ' ' ' '

  "01 (X!2) * ('+34)

  #A! (X!2) * (/564)

  Kmap-SUM

 

"01 * X,!,2 X!,2, X,!2,

  "01 * X ! 2

  Kmap-CARRY

 

#A! * X! X2 !2

Full Adder ui!" A#$-%R 

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 $he below implementation shows implementing the full adder with A78-9 gates instead of

using X9 gates. $he basis of the circuit below is from the above :map.

  Circuit-SUM

 

Circuit-CARRY

 

Full Adder ui!" A#$-%R 

  Circuit-SUM

 

Circuit-CARRY