Number Systems & Boolean

A 3-input majority logic gate has inputs $X, Y$ and $Z$. The output $F$ of the gate is logic ' 1 ' if two or more of the inputs are logic ' 1 '. The output $F$ is logic ' 0 ' if two or more of the inputs are logic '0'. W...

For the Boolean function $F(A, B, C, D) = \sum m(0,2,5,7,8,10,12,13,14,15)$, the essential prime implicants are _________.

A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers...

In a number system of base $r$, the equation $x^2 - 12x + 37 = 0$ has $x = 8$ as one of its solutions. The value of $r$ is _______.

Consider a Boolean gate (D) where the output Y is related to the inputs A and b as, Y = A + $$\overline B $$, where + denotes logical OR operation. The Boolean inputs '0' and '1' are also available separately. Using inst...

Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.

$P, Q$ and $R$ are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1 's complement and 2 's complement representation, respectively. The 6 -bit 2 's complement represent...

A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum of products is given by F = $$\overline A .\overline B .\overline C + \overline A .B.\overline C + A.\overline B .\overline C $$ w...

Which one of the following gives the simplified sum of products expression for the Boolean function $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ where $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ are minterms corresponding to the in...

The following five instructions were executed on an 8085 microprocessor. MVI A, 33H MVI B, 78H ADD B CMA ANI 32H The Accumulator value immediately after the execution of the fifth instruction is

The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is

The Boolean expression F(X, Y, Z)= $$\overline X Y\overline Z + X\overline {Y\,} \overline Z + XY\overline Z + XYZ$$ converted into the canonical product of sum (POS)from is

A function of Boolean variables X,Y and Z is expressed in terms of the min-terms as F(X, Y, Z)=$$\sum\limits_{}^{} {} $$m(1,2,5,6,7) Which one of the product of sums given below is equal to the funtion F(X, Y, Z)?

A 3-input majority gate is defined by the logic function M (a,b,c) = ab+bc+ca. Which one of the following gates is represented by the function M$$\left( {\overline {M\left( {a,b,c} \right),} M\left( {a,b,\overline c } \r...

The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to

Consider the Boolean function, F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline {x\,} \,\overline y \,$$ $$\overline z $$ Which one of the following is the complete set of essenti...

The number of bytes required to represent the decimal number 1856357 in packed BCD (Binary Coded Decimal) form is __________ .

For an n - variable Boolean function maximum number of prime implicants is

In the sum of products function f (x,y,z) = $$\sum {} $$m (2,3,4,5), the prime implicants are

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state...

If 137+276=435 how much is 731+672?

If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$$ $$\left\{ {\overline X + \overline Z (X + Y)} \right\} = 1,$$ then

An 8085 assembly language program is given below. Line 1: MVI A, B5H 2: MVI B, 0EH 3: XRI 69H 4: ADD B 5: ANI 9BH 6: CPI 9FH 7: STA 3010H 8: HLT The contents of the accumulator just after execution of the ADD instruction...

The Boolean expression Y= $$\overline A \,\overline B \,\overline C \,D + \overline A BC\overline D + A\overline {B\,} \overline C \,D + AB\overline C \,\overline D $$

X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s complement format. The sum of X and Y represented in two’s complement format using 6 bits is:

The Boolean function Y=AB+CD is to be realized using only 2-input NAND gates. The minimum number of gates required is

A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-5 number is represented by its corresponding 3-bit binary code. For example, the base-5 number 24 will be represented by its BCP c...

Decimal 43 in Hexadecimal and BCD number system is respectively

The Boolean expression for the truth table shown is A B C D 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0

11001, 1001 and 111001 correspond to the 2’s complement representation of which one of the following sets of number?

The Boolean expression AC + B$$\overline C $$ is equivalent to

A Boolean function 'f' of two variables x and y is defined as follows: f(0,0)=f(0,1)=f(1,1)=1;f(1,0)=0 Assuming complements of x and y are not available, a minimum cost solution for realizing F using only 2-input NOR gat...

The range of signed decimal numbers that can be represented by 6-bite 1’s complement number is

If the functions W, X, Y and Z are as follows W= R+$$\overline P Q + \overline R $$ S X = $$X = PQ\overline R \,\overline S + \overline P \,\overline Q \,\overline R \,\overline S + P\overline Q \,\overline R \,\overline...

The number of distinct Boolean expressions of 4 variables is

4-bit 2’s complement representation of a decimal number is 1000. The number is

The contents of Register (B) and Accumulator (A) of 8085 microprocessor are 49H and 3AH respectively. The contents of A and the status of carry flag (CY) and sign flag (S) after executing SUB B instructions are

The 2’s complement representation of –17 is

The Logical expression $$Y = A + \overline A B$$ is equivalent to

The minimized form of the logical expression ($$\overline A \,\overline B \,\overline C + B\overline C + \overline A B\overline C + \overline A BC + AB\overline C )$$

In certain application, four inputs A, B, C, D (both true and complement forms available)are fed to logic circuit, producing an output F which operates a relay. The relay turns on when F(ABCD)=1 for the following states...

Two 2' s complement numbers having sign bits x and y added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the Boolean function.

An equivalent 2’s complement representation of the 2’s complement number 1101 is

A signed integer has been stored in a byte using the 2's complement format. We wish to store the same integer in a 16-bit word. We should

Given the Boolean function F in three variables R, S and T as F=$$\,\overline R \,S\overline T + R\overline {S\,} T + RST$$ (a) Express F in the minimum sum-of-products from. (b) Express F in the minimum product-of-sums...

The minimum number of NAND gates required to implement the Boolean function $$A + A\overline B $$ $$ + A\overline B C$$ is equal to

An 'Assembler' for a microprocessor a used for

2’s complement representation of a 16-bit number (one sign bit and 15 magnitude bits) is FFFI. Its magnitude in decimal representation is

Boolean expression for the output of XNOR (equivalence) logic gate with inputs A and B is

A combinational circuit has three inputs A, B and C and an output F. F is true only for the following input combinations? A is false and B is true A is false and C is true A, B and C are all false A, B and C are all true...

The four variable function f is given in terms of min-terms as: f (A B C D ) = $$\sum {} $$m (2,3,8,10,11,12,14,15 .) Using the K-map minimize the function in the sum of products form. Also, given the realization using o...

The number of Boolean functions that can be generated by n variable is equal to:

The minimum function that can detect a "divisible by 3" 8421 BCD code digit (representation is D 8 D 4 D 2 D 1 ) is given by:

Indicate which of the following logic gates can be used to realize all possible combinational Logic functions:

The minimum number of 2-input NAND gates required to implement the Boolean function Z=A$$\overline {B\,} $$C, assuming that A, B and C are available, is

The Boolean function A+BC is a reduced form of

Minimum number of 2-input NAND gates required to implement the function, f=($$\overline X $$+$$\overline Y $$)(Z+W) is

For the identity AB+$$\overline A $$ C + BC= AB + $$\overline A $$ C, The dual form is

The subtraction of a binary number Y from another binary number X, done by adding the 2's complement of Y to X, result in a binary number without overflow. This implies that the result is: