General

Question 1

De Morgan Laws

Answer 1

1) NOT(x AND y) = NOT(x) OR NOT(y) 2) NOT(x OR y) = NOT(x) AND NOT(y)

Question 2

(x NAND y) =?

Answer 2

(x NAND y) =NOT(x AND y)

Question 3

NAND(1 1) =?

Answer 3

Question 4

NAND(1 0) =?

Answer 4

Question 5

NAND(1 1) =?

Answer 5

Question 6

Sheffer stroke

Answer 6

In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as “not both”. It is also called nand (“not and”) or the alternative denial, since it says in effect that at least one of its operands is false. In digital electronics, it corresponds to the NAND gate. It is named after Henry M. Sheffer

Question 7

NAND stands for

Answer 7

Not AND… NAND

Question 8

Any boolean function can be represented using only NAND gates. Proof:

Answer 8

All boolean functions are made up of OR, AND and NOT

so as OR (a,b) =NOT(a) AND NOT(b)

We only need to show that AND and NOT can be represented using NAND

^{<span>(</span>}_{<span>*</span>}^{<span>) </span>}NOT(a) = NAND(a,a)

So only need to express AND:

AND(a,b) =^(*) NOT(NAND(a,b))