Konular

2) Consider A6 -variable Boolean Function F=f_(1)(x_(1),x_(2),x_(3),x_(4))cdot F_(2)(x_(4),x_(5),x_(3)) Where F_(1)=prod

Soru

2) Consider a6 -variable Boolean function f=f_(1)(x_(1),x_(2),x_(3),x_(4))cdot f_(2)(x_(4),x_(5),x_(3)) where f_(1)=prod (1,2,3,5,7,12,14)-X_(1) is the most significant bit, and f_(2)=prod (3,4,5,6,7)-X_(4) is the most significant bit. a) Obtain a minimal product-of-sum (POS)expression for f. b) Implement f using only two-input NAND (NAND-2) gates; use minimal number o gates. Use only variables as inputs (not their negated forms).

Çözüm

4.6 (188 Oylar)

İzzet

Uzman doğrulaması

Usta · 5 yıl öğretmeni

Cevap

a) To obtain a minimal product-of-sum (POS) expression for f, we need to find the prime implicants for each function

and

.For

, the given expression is

. This means that

is equal to 1 for all combinations of

except when

is 1. The prime implicants for

are:

For

, the given expression is

. This means that

is equal to 1 for all combinations of

except when

is 1. The prime implicants for

are:

Now, we can write the POS expression for

as:

b) To implement

using only two-input NAND (NAND-2) gates, we can use the following steps:1. Create a NAND-2 gate with inputs

and

. The output of this gate will be

.2. Create a NAND-2 gate with inputs

and

. The output of this gate will be

.3. Create a NAND-2 gate with inputs

and

. The output of this gate will be

.4. Create a NAND-2 gate with inputs

and

. The output of this gate will be

.5. Create a NAND-2 gate with inputs

and $x_{7