How JustAnswer Works:
  • Ask an Expert
    Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.
  • Get a Professional Answer
    Via email, text message, or notification as you wait on our site. Ask follow up questions if you need to.
  • 100% Satisfaction Guarantee
    Rate the answer you receive.
Ask Andy Your Own Question
Andy
Andy, Computer Consultant
Category: Computer
Satisfied Customers: 23538
Experience:  11yr exp, Comp Engg, Internet expert, Web developer, SEO
16465236
Type Your Computer Question Here...
Andy is online now
A new question is answered every 9 seconds

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.
Hello, PLEASE FIND YOUR ANSWER BELOW.
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


---------------------------------------------------------------------------------
Click on the ACCEPT button so that I get paid for my work.
Please leave a Positive Feedback if my answer helped you.
----------------------------------------------------------------------------------
Andy and 6 other Computer Specialists are ready to help you