JEE Main & Advanced Physics Semiconducting Devices Combination of Logic Gates

Combination of Logic Gates

Category : JEE Main & Advanced

(1) The 'NAND' gate : From 'AND' and 'NOT' gate

 

 

Boolean expression and truth table : \[Y=\overline{A\cdot B}\]  

 

A B \[Y'=A\cdot B\] Y
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0

 

(2) The 'NOR' gate : From 'OR' and 'NOT' gate

 

 

 

Boolean expression and truth table : \[Y=\overline{A+B}\]  

 

A B \[Y'=A+B\] Y
0 0 0 1
0 1 1 0
1 0 1 0
1 1 1 0

 

(3) The 'XOR' gate : From 'NOT', 'AND' and  'OR' gate. Known as exclusive OR gate. or The logic gate which gives high output (i.e., 1) if either input A or input B but not both are high (i.e. 1) is called exclusive OR gate or the XOR gate. It may be noted that if both the inputs of the XOR gate are high, then the output is low (i.e., 0).

 

 

 

Boolean expression and truth table : \[Y=A\oplus B=\bar{A}B+A\overline{B}\]  

 

A B Y
0 0 0
0 1 1
1 0 1
1 1 0

 

(4) The exclusive nor (XNOR) gate XOR + NOT \[\xrightarrow{\,\,\,\,\,\,\,\,\,\,}\] XNOR

 

 

 

Boolean expression : \[Y=A\odot =\bar{A}\,\bar{B}+AB\]

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