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# a. Explain the relationship between an AND gate and a NAND

### Resolved Question:

a.    Explain the relationship between an AND gate and a NAND gate in terms of Boolean Algebra and draw truth tables for both types of gate

b.    Explain the relationship between an OR gate and a NOR gate in terms of Boolean Algebra and draw truth tables for both types of gate
Submitted: 8 years ago.
Category: Computer
Expert:  Andy replied 8 years ago.
Have a nice day.

A.

AND gate: If all the inputs of the And gate are 1(true) then the output is 1(true). If Any input of the AND gate is 0 (false), then the output is 0 (false)
NAND gate: If any of the inputs of the Nand gate are 0(false) then the output is 1(true). If all inputs of the NAND gate are 1 (true), then the output is 0 (false)

in terms of Boolean algebra, relationship between AND and NAND is: AND = ~NAND
i.e. AND is invert of NAND

Truth table: AND Gate.
Inputs Output
A B C D
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1

Truth table: NAND Gate.
Inputs Output
A B C D
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0

B.
OR gate: If all the inputs of the OR gate are 0(false) then the output is 0(false). If Any input of the OR gate is 1 (true), then the output is 1 (true)

NOR Gate: If all the inputs of the NOR gate are 0(false) then the output is 1(true). If Any input of the NOR gate is 1 (true), then the output is 0 (false)

in terms of Boolean algebra, relationship between OR and NOR is: OR= ~NOR
i.e. OR is invert of NOR

Truth Table: OR Gate.
Inputs Output
A B C D
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1

Truth Table: NOR Gate.
Inputs Output
A B C D
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0

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