# Recent questions tagged boolean-algebra

1
The possible number of Boolean function of $3$ variables $X,Y$ and $Z$ such that $f(X,Y,Z) = f(X’,Y’,Z’)$ $8$ $16$ $64$ $32$
1 vote
2
In Boolean algebra $1+1+1+1\dots\dots 800$ times ones $=$ ______ . $1$ $0$ $11$ $800$
3
Which of the following logic expression is incorrect? $1\oplus0=1$ $1\oplus1\oplus0=1$ $1\oplus1\oplus1=1$ $1\oplus1=0$
1 vote
4
Which will be the equation of simplification of the given K-map? $AB' + B'CD' + A'B'C'$ $AB' + A'B'D' + A'B'C'$ $B'D' + AB' + B'C'$ $B'D' + A'B'C' + AB'$
5
If $B$ is a Boolean algebra, then which of the following is true? $B$ is a finite but not complemented lattice $B$ is a finite, complemented and distributive lattice $B$ is a finite,distributive but not complemented lattice $B$ is not distributive lattice
6
In digital logic, if $A\oplus B=C$, then which one of the following is true? $A\oplus C=B$ $B\oplus C=A$ $A\oplus B\oplus C=0$ Both (A) and (B)
1 vote
7
If $A\oplus B=C$, then which one of the following is true? $A\oplus C=B$ $B\oplus C=A$ $A\oplus B\oplus C=0$ Both (A) and (B)
8
The value of the Boolean expression (with usual definitions) $(A’BC’)’ +(AB’C)’$ is $0$ $1$ $A$ $BC$
9
What is the time complexity for checking whether an assignment of truth values to variables $x_1,\dots ,x_n$ satisfies a given formula $f(x_1\dots,x_n)$? $O(2^n)$ $O(g(n))$ where $g$ is a polynomial $O(log(n))$ None of the above
10
$(a) A = 101010$ and $B = 011101$ are $1’s$ complement numbers. Perform the following operations and indicate whether overflow occurs. $(i) A + B$ $(ii) A − B$ $(b)$ Repeat part $(a)$ assuming the numbers are $2’s$ complement numbers.
11
Simplify the following expression AB’C + A’BC + A’B’C Solution given is A’C + B’C can someone show me how?
12
f(A,B,C,D)=∏M(0,1,3,4,5,7,9,11,12,13,14,15) is a max-term representation of a Boolean function f(A,B,C,D) where A is the MSB and D is the LSB. The equivalent minimized representation of this function is (A+C¯+D)(A¯+B+D)(A+C¯+D)(A¯+B+D) AC¯D+A¯BD+A¯BC A¯CD¯+AB¯CD¯+AB¯C¯D¯ (B+C¯+D)(A+B¯+C¯+D)(A¯+B+C+D)
1 vote
13
prove that $x’ \oplus y = x \oplus y’ = (x \oplus y)’ = xy+x’y’$
14
Prove that $x \oplus 1$ = x’ and $x \oplus 0$ = x.
15
Show that if xy = 0, then $x\oplus y$ = x + y.
16
Simplify the Following boolean function by means of the tabulation method. (a) P(A,B,C,D,E,F,G)=$\sum(20,28,52,60)$ (b) P(A,B,C,D,E,F,G)= $\sum(20,28,38,39,52,60,102,103,127)$ (C) P(A,B,C,D,E,F) = $\sum(6,9,13,18,19,25,27,29,41,45,57,61)$
17
Implement the following boolean function F together with the don’t-care conditions d using no more than two NOR gates. Assume both normal and the compliment inputs are available. F(A,B,C,D) = $\sum(0,1,2,9,11)$ $d(A,B,C,D) = \sum(8,10,14,15)$
18
A logic circuit implements the following Boolean function: F = A’C + AC’D’ it is found that the circuit input combination A=C=1 can never occur. Find a simpler expression for F using the proper don't-care conditions.
19
Simplify the boolean function F together with the don’t care conditions d in (1) sum of products and (2)product of sums. (A) $F(w,x,y,z) = \sum(0,1,2,3,7,8,10)$ $d(w,x,y,z) = \sum(5,6,11,15)$ (b) $F(A,B,C,D) = \sum (3,4,13,15)$ $d(A,B,C,D) =\sum(1,2,5,6,8,10,12,14)$
20
Simplify the following boolean function F together with the don’t care condition d; then express the simplified function in the sum of minterms. (a)$F(x,y,z)=\sum(0,1,2,4,5)$ $d(x,y,z)= \sum(3,6,7)$ (b) $F(A,B,C,D) = \sum(0,6,8,13,14)$ $d(A,B,C,D) = \sum(2,4,10)$ (C) $F(A,B,C,D) = \sum(1,3,5,7,9,15)$ $d(A,B,C,D)= \sum(4,6,12,13)$
Implement the function F with the Following two level Forms: NAND-AND, AND-NOR, OR-NAND, AND NOR-OR. F(A,B,C,D) = $\sum(0,1,2,3,4,8,9,12)$