What is the role of logic ates in compute hardware Differentiate between NAND gate and NOR gate also draw truth tables for each?

Answer 1

"What is the role of logic gate in computer hardware?"

Think of a computer as a box with a number of electrical signals coming in to it and a number going out of it. Immediately inside the box, associated with those signal wires, is some specialized circuitry whose purpose is (generally) to translate between the idiosyncratic electrical characteristics of the outside world signaling and the consistent internal representation of those signals as Boolean expressions. Everything else inside - everything - is built out of logic gates. So they are pretty fundamental. They are used in several roles:

- as memory cells, e.g. in RAM or ROM

- controling information flow, e.g. the PCI or DDR3 bus control circuitry

- as elements of the computing engine itself

--- The Arithmetic Logic Unit (ALU)

--- The Working Register Array

--- the Instruction Decode and Execution Unit

--- the Memory Management Unit (MMU)

Waaay back, in the 50's if not the 40's or earlier, when a lot of the basic work on mechanising Boolean Algebra was done, a very smart guy had a startling revelation: every Boolean computational circuit you would ever want to build could be constructed using only 2 input NAND gates. This lemma is known (in CS) as the Schmidt Orthogonality Principle. To make a practical computing device, the only other element you need is a means of harnessing time to provide sequential stepping controls. This takes some specialized circuitry, but also is a very tiny component of the over-all system - the System Clock.

As to the specifics of NAND gates - and NOR gates, and so on, they obey very simple rules:

For f(A,B) = ~(A & B),

f(0,0) = 1

f(0,1) = 1

f(1,0) = 1

f(1,1) = 0

For f(A,B) = ~(A + B),

f(0,0) = 1

f(0,1) = 0

f(1,0) = 0

f(1,1) = 0

In English,

- the NAND output is TRUE iff any of its inputs are FALSE

- the NOR output is FALSE iff any of its inputs are TRUE

(NB: the term 'iff' means 'if and only if' - it is not a typo)

As an exercise for the reader, given the Schmidt Orthogonality Principle, how would you build a 2 input NOR gate functionality using only 2 input NAND gates? XOR? Full Adder?

All other functional blocks are built out of these primitives. Millions of them, in today's computers. A NAND gate can be implemented with 1 transistor having 2 (or more) emitters for the inputs, and 1 more transistor for the inverting output. Real circuits have a few more components, but those are for dealing with the realities that the circuits have to obey essentially analog physics yet behave as though they are digitial.