# Recent questions and answers in Digital Logic

1 vote
1
Consider a $3$-bit counter, designed using $T$ flip-flops, as shown below: Assuming the initial state of the counter given by $\text{PQR}$ as $000$, what are the next three states? $011,101,000$ $001,010,111$ $011,101,111$ $001,010,000$
2
Consider the following representation of a number in $\text{IEEE 754}$ single-precision floating point format with a bias of $127$. $S: 1\quad\quad E:\; 10000001\quad\quad F:\;11110000000000000000000$ Here, $S, \;E$ and $F$ denote ... components of the floating point representation. The decimal value corresponding to the above representation (rounded to $2$ decimal places) is ____________.
3
Let the representation of a number in base $3$ be $210$. What is the hexadecimal representation of the number? $15$ $21$ $D2$ $528$
1 vote
4
The format of the single-precision floating point representation of a real number as per the $\text{IEEE 754}$ ... $=00000000$ and mantissa $=0000000000000000000000001$ exponent $=00000001$ and mantissa $=0000000000000000000000000$ exponent $=00000001$ and mantissa $=0000000000000000000000001$
5
If the numerical value of a $2$-byte unsigned integer on a little endian computer is $255$ more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer? $0\text{x}6665$ $0\text{x} 0001$ $0\text{x} 4243$ $0\text{x} 0100$
1 vote
6
Which one of the following circuits implements the Boolean function given below? $f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6$, where $m_i$ is the $i^{\text{th}}$ minterm.
7
Consider the following Boolean expression. $F=(X+Y+Z)(\overline X +Y)(\overline Y +Z)$ Which of the following Boolean expressions is/are equivalent to $\overline F$ (complement of $F$)? $(\overline X +\overline Y +\overline Z)(X+\overline Y)(Y+\overline Z)$ $X\overline Y + \overline Z$ $(X+\overline Z)(\overline Y +\overline Z)$ $X\overline Y +Y\overline Z + \overline X \overline Y \overline Z$
8
If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________
9
Consider a Boolean function $f(w,x,y,z)$ such that $\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}$ The number of literals in the minimal sum-of-products expression of $f$ is _________
10
Booth's coding in $8$ bits for the decimal number $-57$ is: $0-100+1000$ $0-100+100-1$ $0-1+100-10+1$ $00-10+100-1$
1 vote
11
How many Addition and Subtraction are required if you perform multiplication of $5$ (Multiplicand) and $-30$(Multiplier) using Booth Algorithm? $2,1$ $1,2$ $1,1$ $2,2$
1 vote
12
I understand booth's algorithm, but what is the meaning of this question?
13
Please Explain the Rule to find number of additions and subtractions required for multiplication of two given numbers.
14
1) In Booth's bit-pair recording technique how to multiply a multiplicand with 2? 2) In booth's algorithm for multiplication/Booth's bit-pair recording of multipliers, the sign bit extension of the multiplicand i.e. we must extend the sign-bit value of the multiplicand to the left ... +2 I don't know Also, why is the sign bit extended? Will we get the correct answer if we don't extend sign bit?
The characteristic equation of a $\text{T}$ flip-flop is : $Q_{n+1}=T\overline Q_n+\overline T Q_n$ $Q_{n+1}=T+Q_n$ $Q_{n+1}=TQ_n$ $Q_{n+1}=\overline T$\overline Q_n$The symbols used have the usual meaning. 0 votes 3 answers 18 In$\text{RS}$flip-flop, the output of the flip-flop at time$(t+1)$same as the output at time$t$, after the occurrence of a clock pulse if :$S=R=1S=0, R=1S=2, R=0S=R=0$65 votes 4 answers 19 Minimum No of Gates NAND/NOR Ex-OR Ex-Nor Half Adder Half Subtractor Full Adder Full Subtractor NAND ? ? ? ? ? ? NOR ? ? ? ? ? ? 62 votes 8 answers 20 Consider a carry look ahead adder for adding two n-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is$\Theta (1)\Theta (\log(n))\Theta (\sqrt{n})\Theta (n)$) 17 votes 7 answers 21 Consider three$4$-variable functions$f_1, f_2$, and$f_3$, which are expressed in sum-of-minterms as$f_1=\Sigma(0,2,5,8,14),f_2=\Sigma(2,3,6,8,14,15),f_3=\Sigma (2,7,11,14)$For the following circuit with one AND gate and one XOR gate the output function$f$can be expressed as:$\Sigma(7,8,11)\Sigma (2,7,8,11,14)\Sigma (2,14)\Sigma (0,2,3,5,6,7,8,11,14,15)$1 vote 3 answers 22 The range of the numbers which can be stored in an eight bit register is$-128$to$+127-128$to$+128-999999+ \: +999999$none of these 0 votes 2 answers 23 If the input$\text{J}$is connected through$\text{K}$input of$\text{J-K}$, then flip-flop will behave as a D type flip-flop T type flip-flop S-R flip-flop Toggle switch 0 votes 3 answers 24 If a clock with time period$“T”$is used with$n$stage shift register, then output of final stage will be delayed by$nT$sec$(n-1)T$sec$n/T$sec$(2n-1)T$sec 0 votes 2 answers 25 A sequential circuit using D flip-flop and logic gates is shown in Figure, where$X$and$Y$are the inputs and$Z$is the output. The circuit is$\text{S-R}$Flip-flop with inputs$X = R$and$Y=S\text{S-R}$Flip-flop with inputs$X = S$and$Y=R\text{J-K}$Flip-flop with inputs$X = J$and$Y=K\text{J-K}$Flip-flop with inputs$X = K$and$Y=J$0 votes 4 answers 26 A$4$bit ripple counter and a$4$bit synchronous counter are made using flip-flops having a propagation delay of$10$ns each. If the worst case delay in the ripple counter and the synchronous counter be$R$and$S$respectively, then$R = 10$ns,$S = 40$ns$R = 40$ns,$S = 10$ns$R = 10$ns,$S = 30$ns$R = 30$ns,$S = 10$ns 1 vote 2 answers 27 A sequential circuit using D flip-flop and logic gates is shown in Figure, where$X$and$Y$are the inputs and$Z$is the output. The circuit is$\text{S-R}$Flip-flop with inputs$X = R$and$Y=S\text{S-R}$Flip-flop with inputs$X = S$and$Y=R\text{J-K}$Flip-flop with inputs$X = J$and$Y=K\text{J-K}$Flip-flop with inputs$X = K$and$Y=J$0 votes 1 answer 28 The period of a signal is$100$ms, then the frequency of this signal in kilohertz is ______$1010^{-1}10^{-2}10^{-3}$0 votes 3 answers 29 Simplified expression/s for following Boolean function$F(A,B,C,D)=\Sigma(0,1,2,3,6,12,13,14,15)$is/are$A’B’+AB+A’C’D’A’B’+AB+A’CD’A’B’+AB+BC’D’A’B’+AB+BCD’$Choose the correct answer from the options given below:$(a)$only$(b)$only$(a)$and$(b)$only$(b)$and$(d)$only 1 vote 1 answer 30 is given ans correct ? 0 votes 0 answers 31 A$4$bit ripple counter and a$4$bit synchronous counter are made using flip-flops having a propagation delay of$10$ns each. If the worst case delay in the ripple counter and the synchronous counter be$R$and$S$respectively, then$R = 10$ns,$S = 40$ns$R = 40$ns,$S = 10$ns$R = 10$ns,$S = 30$ns$R = 30$ns,$S = 10$ns 0 votes 1 answer 32 Odd parity of word can be conveniently tested by OR gate AND gate NOR gate XOR gate 1 vote 1 answer 33 A sequential circuit outputs a$\text{ONE}$when an even number$(>0)$of one’s are input; otherwise the output is$\text{ZERO}.$The minimum number of states required is$0123$0 votes 1 answer 34 To build a mod-$19$counter the number of flip-flop required is$3578$0 votes 1 answer 35 Which of the following conditions must be met to avoid race around problem?$\Delta t< t_{p}< TT>\Delta t> t_{p}2t_{p}< \Delta t< T$none of these 0 votes 1 answer 36 The excess$3$code is also called cyclic redundancy code weighted code self complimenting code algebraic code 0 votes 2 answers 37 How many flip-flop are needed to divide the input frequency by$64$?$4568$1 vote 1 answer 38 A decimal has$25$digits. The number of bits needed for its equivalent binary representation is approximately$50744060$0 votes 1 answer 39 In a ripple counter using edge-triggered$JK$flip-flops, the pulse input is applied to Clock input of all flip-flops$J$and$K$input of one flip-flop$J$and$K$input of all flip-flops Clock input of one flip-flop 0 votes 1 answer 40 How many$2$-input multiplexers are required to construct a$2^{10}$input multiplexer?$10233110127\$