DIGITAL ELECTRONIC

 

 

QS.1(i) What is the binary equivalent of the decimal number (368)₁₀

Ans.

The Binary equivalent of the Decimal number (368)₁₀ is (101110000)_2.

 

QS.1(ii) The decimal equivalent of hex number 1A53 is

Ans. The decimal equivalent of Hex Number 1A53 is 6739

(Conversion from Hex Number to Decimal Number is given below)

1 A 5 3 Hexadecimal

16³ 16² 16¹ 16° Weights

(1A53)16 = (1X16³) + (10 X 16²) + (5 X 16¹) + (3 X 16º)

= 4096 + 2560 + 80 + 3

= 6739

 

QS.2 The simplification of the Boolean expression (ABC)+ (ABC) is

Ans.  The Boolean expression is (ABC)+ (ABC) is equivalent to 1

(ABC)+ (ABC) = A + B +C + A + B +C = A + B + C + A + B + C

= (A+ A )(B+ B )(C+C ) = 1.1.1 = 1

 

QS.3The Gray code for decimal number 6 is equivalent to?

Ans. The Gray code for decimal number 6 is equivalent to 0101

Decimal number 6 is equivalent to binary number is 0110

 

QS.4. Simplify the following expression into sum of products using Karnaugh map

F(A,B,C,D) = _(1,3,4,5,6,7,9,12,13).

Ans. Simplification of the following expression into sum of products using Karnaugh

Map:

F(A,B,C,D) = S (1,3,4,5,6,7,9,12,13)

Karnaugh Map for the expression F(A,B,C,D) = S (1,3,4,5,6,7,9,12,13)

is shown in Fig.5(a). The grouping of cells is also shown in the Figure.

Fig.4(a)

 

QS.5 Simplify and draw the logic diagram for the given expression

F = ABC+ ABC+ ABC+ ABC+ ABC.

Ans. Simplification of the logic expression

F = ABC + AB C + ABC + A BC + A B C

F = ABC + AB C + ABC + A BC + A B C

F = A + B +C + ( A + B )C + ABC + A ( B +C ) + A B C

(Q ABC = A + B +C and AB = A + B by using Demorgan’s Law)

= A + B +C + AC + B C + ABC + A B + AC + A B C

= A + AC+ B + B C +C + AC + ABC +A B + A B C

= A (1+C)+ B (1 + C) +C (1 + A) + ABC + A B + A B C

= A + B +C + ABC + A B + A B C {Q (1+C) = 1 and (1+A) = 1}

= ( A + A B ) + B (1 + AC) +C (1+ AB)

= ( A + B )+ B +C {Q ( A + A B ) = ( A + B ); (1+AC) = 1 and (1+ AB) =1}

F = ( A + B +C ) (Q B + B = B )

The logic diagram for the simplified expression F = ( A + B +C ) is given in fig.6 (a)

Fig.5(a) Logic diagram for the expression F = ( A + B +C )