the ripple counter shown in the given figure 2 works as a or in the modulo 6 ripple counter shown in the figure the output of the 2 input ?
Unit Exercise – 2

A computer has the following negative number stored in binary form as shown. the wrongly stored number is

(a) -37 as 1101 1011
(b) -89 as 1010 0111
(c) -48 as 1110 1000
(d) -32 as 1110 0000

if X = 1 in the logic equation

e (X + Z{Y +(Z + Y)}] [X + Z(X + Y)] = 1, Then
(a) Y = Z
(b) Y = Z
(c) Z = 1
(d) Z = 0

If the input x₃, x₂, x₁, x_o to the ROM in figure are 8-4-2-1 BCD number, then the output Y₃Y₂Y₁Y₀ are

(a) gray code number
(b) 2-4-2-1 BCD number
(c) excess 3 code number
(d) none of the above

In figure the j and k inputs of all the four flip-flops are made high. the frequency of the signal at output y is

(a) 0.833 KHz
(b) 1.0 kHz
(c) 0.91 kHz
(d) 0.77 kHz

Consider the CMOS circuit shown in figure. it acts as a

(a) negative NAND
(b) positive NAND
(c) negative NOR
(d) positive NOR

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

(a) 25, 9 and 57 respectively
(b) – 6, -6 and -6 respectively
(c) -7, -7 and -7 respectively
(d) -25, -9 and -57 respectively

The Boolean expression AC + BC is equivalent to

(a) AC + BC + AC
(b) BC + AC + BC + ACB
(c) AC + BC + BC + ABC
(d) ABC + ABC + ABC + ABC

Expression A + AB + A BC + ABCD + ABCDE would be simplified to

(a) A + AB + CD + E
(b) A + B + CDE
(c) A + BC + CD + DE
(d) A + B + C + D + E

For the circuit shown in the following figure I₀ – I₃ are inputs to the 4 : 1 multiplexer R (MSB) and S are control bits

the output Z can be represented by
(a) PQ + PQS + QRS
(b) PQ + PQR + PQS
(c) PQR + PQR + PQRS + QRS
(d) PQR + PQRS + PQ RS + QRS

A 4-bit right shift register is initialized to value 1000 for (Q₃, Q₂, Q₁, Q₀). The D input is derived from Q₀, Q₂ and Q₃ through two XOR gates as shown in figure. the pattern 1000 will appear at

(a) 3rd pulse
(b) 7th pulse
(c) 6th pulse
(d) 4th pulse

A certain logic family has the following voltage parameters;

V_IH(MIN) = 3.5 V, V_IL(MAX) = 1.0 V, V_OH(MIN) = 4.9 V and V_OL(MAX) = 0.1 V. The largest positive-going and negative-going spike, that can be tolerate, is respectively
(a) 1.4 v, 0.9 v
(b) 0.9 v, 1.4 v
(c) 3.9 v, 3.4 v
(d) none of these

The two numbers represented in signed 2’s complement form are p = 11101101 and Q =11100110. If Q is subtracted from p, the value obtained in signed 2’s complement form is

(a) 100000111
(b) 00000111
(c) 11111001
(d) 111111001

X = ?

(a) AB
(b) AB
(c) AB
(d) 0

The circuit shown in figure converts

(a) BCD to binary code
(b) binary to excess-3 code
(c) excess-3 to gray code
(d) gray to binary code

In figure, the LED

(a) emits light when both S₁ and S₂ are closed
(b) emits light when both S₁ and S₂ are open
(c) emits light when only S₁ or S₂ is closed
(d) does not emit light, irrespective of the switch positions

The CMOS circuit shown in figure, implements

(a) AB + CD + E
(b) (A + B) (C + D) E
(c) AB + CD + E
(d) (A + B) (C + D) E

7-bit hamming code groups consisting of 4 formation bits and 3 parity bits is transmitted. the group 1101100 is received in which at most a single has occurred. the transmitted code is

(a) 1111100
(b) 1100100
(c) 1001100
(d) 1101000

In the following circuit, X is gives by

(a) X = ABC + ABC + ABC + ABC
(b) X = ABC + ABC + ABC + ABC
(c) X = AB + BC + AC
(d) X = AB + BC + AC

The mod-number of the asynchronous counter shown in figure is

(a) 24
(b) 48
(c) 25
(d) 36

In the modulo-6 ripple counter shown in figure, the output of the 2-input gate is used to clear the j-k flip-flops.

The 2-input gate is
(a) a NAND gate
(b) a NOR gate
(c) an OR gate
(d) an AND gate

In the DRAM cell in figure the V_T of the n-MOSFET is 1 v. for the following three combinations of WL and BL voltages.

(a) 5 V; 3 V; 7 V
(b) 4 V; 3 V; 4 V
(c) 5 V; 5 V; 5 V
(d) 4 V; 4 V; 4 V

Consider the signed binary number A = 01000110 and B = 11010011, where B is in 2’s complement and MSB is the sign bit. in list I operation is given and in list II resultant binary number is given, match them and find the correct answer using the codes given below the lists.

List I List II

A + B 1. 1 0 0 0 1 1 0 1
A – B 2. 1 1 1 0 0 1 1 1
B – A 3. 0 1 1 1 0 0 1 1
– A – B 4. 1 0 0 0 1 1 1 0
0 0 0 1 1 0 1 0
0 0 0 1 1 0 0 1
0 1 0 1 1 0 1 1

Codes
P                      Q                           R                  S
(a)          5                      7                             4                  2
(b)          6                       3                           1                    2
(c)         6                        7                           1                    3
(d)         5                        3                            4                    2

Consider the signed binary number A = 01010110 and B = 11101100 where, B is the 1’s complement and MSB is the sign bit. in list I opertion is given, and in list II resultant binary number is given match them and find the correct answer using the codes below the lists.

List I List II

A + B 1. 0 1 0 0 0 0 1 1
B – A 2. 0 1 1 0 1 0 0 1
A – B 3. 0 1 0 0 0 0 1 0
– A – B 4. 1 0 0 1 0 1 0 1
1 0 1 1 1 1 0 0
1 0 0 1 0 1 1 0
1 0 1 1 1 1 0 1
0 1 1 0 1 0 1 0

Codes
P                     Q                  R                 S
(a)         3                       4                  2                  5
(b)         3                        6                  8                  7
(c)         1                         4                  8                  7
(d)         1                        6                   2                  5

The minimum number of 2 to 1 multiplexers equired to realize a 4 to 1 multiplexer is

(a) 1
(b) 2
(c) 3
(d) 4

An ECL gate exhibits the following characteristics V_OH(MIN) = – 0.8 V, V_OL(MAX)= 2.0 V, and V_NL= V_NH = 0.5 V. the values of V_IH(MIN)and V_IL(MAX) would be respectively,

(a) -0.3 v, 2.5 v
(b) -1.3 v, -1.5 v
(c) 1.3 v, -1.5 v
(d) 0.3 v, 2.5 v

11001, 1001 and 111001 correspond to the 2’s complement representation of the following set of numbers

(a) 25, 9 and 57 respectively
(b) -6, -6 and -6 respectively
(c) -7, -7 and -7 respectively
(d) -25, -9 and -57 respectively

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 code 010100. in this numbering system, the BCP code 100010011001 corresponds to the following number in base-5 system

(a) 423
(b) 1324
(c) 2201
(d) 4231

In the circuit shown in figure A is a parallel-in parallel-out 4-bit register which loads at the rising edge of the clock C. the input lines are connected to a 40-bit bus, W. its output acts as the input to a 16.4 ROM whose output is floating when the enable input E is 0. A partial table of the contents of the ROM is as follows :

The clock to the register is shown and the data on the W bus at time T₁ is 0110. the data on the bus at time t₂ is
(a) 1111
(b) 1011
(c) 1000
(d) 0010

Z = ?

(a) ABC
(b) A B C
(c) 0
(d) ABC

The logic function implemented by the following circuit at the terminal Out is

(a) P NOT Q
(b) P NAND Q
(c) P OR Q
(d) P NAND Q

A signed integer has been stored in a byte using 2’s complement format. we wish to store the same integer in 16-bit word. we should copy the original byte to the less significant byte of the word and fill the more significant byte with

(a) 0
(b) 1
(c) equal to the MSB of the original byte
(d) complement of the MSB of the original byte

What are the minimum number of 2 to 1 multiplexers required to generate a 2 input AND gate and a 2 input Ex-OR gate ?

(a) 1 and 2
(b) 1 and 3
(c) 1 and 1
(d) 2 and 2

The DTL, TTL, ECL, and CMOS families of digital ICs are compared in the following 4 columns P Q R S

Fan-out is minimum    DTL                     DTL                   TTL                    CMOS
Power consumption is TTL                  CMOS                 ECL                   DTL
Propagation delay is    CMOS               ECL                     TTL                   TTL
minimum
The correct column is
(a) P
(b) Q
(c) R
(d) S

What is the value of Z?

(a) ABC
(b) AB(C + B)
(c) ABC
(d) AB(C + B)

The digital block in figure is realized using two positive edge triggered D flip-flops Assume that for t < t_o, Q₁ = Q₂ = 0. The circuit in the digital block given by

(a) fig (A)
(b) fig. (B)
(c) fig. (C)
(d) fig. (D)

The boolean expression for the truth table shown below is

(a) B(A + C) (A + C)
(b) B (A + C) (A + C)
(c) B (A + C) (A + C)
(d) B (A + C) (A + C)

The boolean function realized by the logic circuit shown is

(a) f = m(0,1,3,5,9,10,14)
(b) f = m (2,3,5,7,8,12,13)
(c) f = m (1,2,4,5,11,14,15)
(d) f = m (2,3,5,7,8,9,12)

Two D flip-flops as shows below are to be connected as a synchronous counter that goes through the following Q₁Q₀ sequence

00 – 01 – 11 – 10 – 00
The inputs D₆ and D₁ respectively, should be connected as
(a) Q₁ and Q_O
(b) Q₀ and Q₁
(c) Q₁Q₀ and Q₁Q_O
(d) Q₁Q_O and Q₁Q_O

For the 4-bit DAC shown in figure the output voltage V_O is

(a) 10 v
(b) 5 v
(c) 4 v
(d) 8 v

if the functions w, x, y and z are as follows :

W = R + PQ + RS
X = PQRS + PQRS + PQRS
Y = RS + PR + PQ + PQ
Z = R + S + PQ + PQR + PQS
Then,
(a) w = z, x = z
(b) w = z, x = y
(c) w = y
(d) w = y = z

The k-map for a boolean functions is shown in figure. the number of essential prime implicants for this function is

(a) 3
(b) 4
(c) 5
(d) 6

What memory address range is not represented by chip # 1 and chip # 2 in figure A₀ to A₁₅ is the figure are the address lines and CS means chip select

(a) 0100 – 02 FF
(b) 1500 – 16 FF
(c) F900 – FAFF
(d) F800 – F9FF

The circuit shown in figure is a 4-bit DAC. the input bits 0 and 1 are represented by 0 and 5 v respectively. the op-amp is ideal but all the resistances and the 5 v inputs have tolerance of +10% the simplification (rounded to the nearest multiple of 5%) for the tolerance of the DAC is

(a) + 35%
(b) + 20%
(c) +10%
(d) + 5%

The boolean expression Y = ABCD + ABCD + ABCD + ABCD can be minimized to

(a) Y = ABCD + ABC + ACD
(b) Y = ABCD + BCD + ABCD
(c) Y = ABCD + BCD + ABCD
(d) Y = ABCD + BCD + ABCD

The boolean expression AC + BC is equivalent to

(a) AC + BC + AC
(b) BC + AC + BC + ACB
(c) AC + BC + BC + ABC
(d) ABC + ABC + ABC + ABC

In the circuit shown in figure is PIPO 4-bit register, which loads at the rising edge of the clock. the input lines are connected to a 4-bit bus. its output acts as the input to a 16 x 4 ROM whose output is floating when the enable input E is 0. a partial table of the contents of the ROM is as follows :

The data on the bus at time t₂ is
(a) 1 1 1 1
(b) 1 0 1 1
(c) 1 0 0 0
(d) 0 0 1 0

The circuit in figure has two CMOS NOR gates. this circuit functions as a

(a) flip-flop
(b) schmitt trigger
(c) monostable multivibrator
(d) astable multivibrator

The boolean expression (x + y) (x + y) (x + y) is equivalent

(a) xy
(b) xy
(c) xy
(d) xy

f = ?

(a) wxyz + wxyz + xy + yz
(b) wxyz + wxyz + xy + yz
(c) wxyz + wxyz + yz + zx
(d) wxyz + wxyz + gz + zx

The three-stage johnson counter as shown in figure is clocked at a constant frequency of f_c from the starting state of Q₂Q₁Q₀ = 101. the frequency of output Q₂Q₁Q_O will be

(a) f_c/4
(b) f_c/8
(c) f_c/2
(d) f_c/6

What are the counting stages (Q₁, Q₂) for the counter shown in the figure below?

(a) 11, 10, 00, 1, 10…………
(b) 01, 10, 11, 00, 01………
(c) 00, 11, 01, 10, 00,………
(d) 01, 10, 00, 01, 10……….

A digital voltmeter uses a 10 MHz clock and has a voltage controlled generator which provides a width of 10 us per volt of unit signal. 10 v of input signal would correspond to a pulse count of

(a) 1500
(b) 750
(c) 1000
(d) 500

Z = ?

(a) A + B + C
(b) ABC
(c) AB + BC + AC
(d) All of these

The 4-to-1 multiplexer shown in figure implements the boolean expression

f(w,x,y,z) = m(4,5,7,8,10,12,15)
The input to I₁ and I₃ will be
(a) yz, y + z
(b) y + z, y * z
(c) y + z, y * z
(d) x + y, y * z

The digital block in figure realized using two positive edge triggered D flip-flop. assume that for t < t₀, Q₁ = Q₂ = 0.

The circuit in the digital block is given by

A 4-bit ripple counter and a 4-bit synchronous counter are made using flip-flops having propagation delay of 10 ns each. if the worst case delay in the ripple counter and the syschronous counter be R and S respectively, then

(a) R = 10 ns, S = 40 us
(b) R = 40 us, S = 10 us
(c) R = 10 us, S = 30 us
(d) R = 30 us, S = 10 us

The step size of the DAC of figure is 0.5 V. The value of R_F is

(a) 1.6 k
(b) 8 k
(c) 800
(d) 1 k

The point P in the following figure is stuck 1. the output f will be

(a) ABC
(b) A
(c) ABC
(d) A

It is desired to generate the following three boolean function :

f₁ = abc + abc + bc
f₂ = abc + ab + abc
f₃ = abc + abc + ac
by using on OR gate array as shown in figure where P₁ and P₅ are the product terms in one or more of the variable a, a, b, b, c and c.
The terms P₁, P₂, P₃, P₄ and p₅ are
(a) ab, ac, bc, bc, ab
(b) ab, bc, ac, ab, bc
(c) ac, ab, bc, ab, bc
(d) All of these

Figure shows a ripple counter using positive edge triggered flip-flops. if the present state of counter is Q₂Q₁Q₀ = 011, then its next state (Q₂Q₁Q₂) will be

(a) 010
(b) 100
(c) 111
(d) 101

A 4-bit modulo-6 ripple counter uses j-k fliop-flop. if the propagation delay of each flip-flop is 50 ns, the maximum clock frequency that can be used is equal to

(a) 5 MHz
(b) 10 MHz
(c) 4 MHz
(d) 20 MHz

A 12-bit (3-digit) DAC that uses the BCD input code has a full scale output of 9.99 v. the value of V_OUT for an input code of 0110 1001 0101 is

(a) 4.11 v
(b) 6.95 v
(c) 7.38 v
(d) 7.88 v

Which of the following boolean expression correctly represents the relation between p, Q, R and M₁?

(a) M₁ = (P OR Q) XOR R
(b) M₁ = (P AND Q) XOR R
(c) M₁ = (P NOR Q) XOR R
(d) M₁ = (P XOR Q) XOR R

A logic circuit consist of two 2 x 4 decoder as shown in figure below.

The output of decoder are as follow:
D₀= 1 when A₀ = 0, A₁ = 0
D₁ = 1 when A₀ = 1, A₁ = 0
D₂ = 1 when A₀ = 0, A₁ = 1
D₃ = 1 when A₀ = 1, A₁ = 1
The value of f(x,y,z) is
(a) zero
(b) z
(c) z
(d) 1

A 4-bit ripple couter and a 4-bit synchronous couter are made by fliap-flops having a propagation delay of 10 us each. if the worst case delay in the ripple couter and the synchronous couter be R and S respectively, then

(a) R = 10 ns, S = 40 us
(b) R = 40 ns, S = 10 ns
(c) R = 10 ns, S = 30 ns
(d) R = 30 ns, S = 10 ns

For the circuit shown, the couter state (Q₁Q₂) follows the sequence

(a) 00, 01, 10, 11, 00…
(b) 00, 01, 10, 00, 01…….
(c) 00, 01, 11, 00, 01………
(d) 00, 10, 11, 00, 10…….

The current rating of a TTL series logic gates are I_OL(MAX)= 8 mA, I_OH(MAX) = – 0.4 mA I_IL(MAX) = – 0.1 mA, I_IH(MAX) = 20 uA

If all gates are 2-input NAND gate, then fan-out is
(a) 10
(b) 20
(c) 60
(d) 80

Refer to the NAND and NOR latches shown in the figure. the inputs (P₁, P₂) for both the latches are first made (0,1) and then after a few seconds, made (1,1). the corresponding stable outputs (Q₁, Q₂) are

(a) NAND : first (0,1) then (0,1) NOR: first (1,0) then (0,0)
(b) NAND : first (1, 0) then (1, 0) NOR : first (1, 0) then (1, 0)
(c) NAND : first (1, 0) then (1, 0) NOR : first (0,1) then (0, 0)
(d) NAND : first (1, 0) then (1,1) NOR : first (0,1) then (0,1)

The MUX shown in figure is 4 x 1 multiplexer. the output Z is

(a) ABC
(b) A * B * C
(c) A * B * C
(d) A + B + C

The present output Q_N of an edge triggered j-k flip-flop is logic 0. if j = 1, then Q_{N + 1}

(a) cannot be determined
(b) will be logic 0
(c) will be logic 1
(d) will race around

The circuit shown in figure is

(a) a MOD-2 couter
(b) a MOD-3 couter
(c) generate sequence 00, 10, 01, 00……..
(d) generate sequence 00, 10, 00, 10, 00………..

The MOSFET circuit shown in figure implements the function

(a) A (B + C)
(b) ABC
(c) A + BC
(d) A BC

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 minmum cost solution for realizing f using only 2-input NOR gates and 2-input OR gates (each having unit cost) would have total cost of
(a) 1 unit
(b) 4 unit
(c) 3 unit
(d) 2 unit

For the circuit of figure consider the statements

Assertion (A) The circuit is sequential.
Reason (R) There is a loop in circuit.
Choose the correct answer.
(a) both A and R are true and R is the correct explanation of A
(b) both A and R are true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

Consider the RTL gate of figure. the transistor parameters are V_CE(SAT)= 0.2 V and B = 50. The logic high voltage is V_H = 3.5 V. if input drive the similar type of gate, the fan-out is

(a) 5
(b) 10
(c) 15
(d) 20

For the logic circuit shown in figure. the simplified boolean expression for the output Y is

(a) A + B + C
(b) A
(c) B
(d) C

The circuit shown in figure has 4 boxes each descrbed by input P,Q,R and output Y,Z with Y = P * Q *R and Z = RQ + PR + QP.

The circuit acts as a 4-bit
(a) adder giving P + Q
(b) Subtractor giving P – Q
(c) subtractor giving Q – P
(d) adder giving P + Q + R

The counter shown in figure is a

(a) MOD-8 up counter
(b) MOD-8 down counter
(c) MOD-6 up counter
(d) MOD-6 down counter

The circuit of figure acts as

(a) astable multivibrator
(b) monostable multivibrator
(c) bistable multivibrator
(d) none of the above

The following binary values were applied to the x and y inputs of NAND latch shown in the figure in the sequence indicated below.

X = 0, = 1, X = 0, Y; X = 1, Y = 1
The corresponsing stable P, Q outputs will be
(a) P = 1, Q = 0; P = 1, Q = 0; P = 1, Q = 0 or P = 0, Q = 1
(b) P = 1, Q = 0; P = 0, Q = 1; P = 0, Q = 1 or P = 0, Q = 1
(c) P = 1, Q = 0; P = 1, Q = 1; P = 1, Q = 0 or P = 0, Q = 1
(d) P = 1, Q = 0; P = 1, Q = 1; P = 1, Q = 1

The logic circuit shown in figure implements

(a) D (A . C + AC)
(b) D (B . C + AC)
(c) D (B . C + AB)
(d) D (B . C. + AB)

The gates G₁ and G₂ in figure have propagation delays of 10 ns and 20 ns respectively. if the input V_I makes an abrupt change from logic 0 to 1 at time t = t₀ then the output waveform V_O is
The circuit shown in figure implements the function

(a) ABC + ABC
(b) ABC + (A + B + C)
(c) ABC + (A + B + C)
(d) none of these

A 4-bit D/A converter is connected to a free- runnung 3-bit up counter, as shown in the following figure. which of the following waveforms will be observed at V₀?

In the figure shown above, the ground has been shown by the symbol

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

(a) s-r flip-flop with inputs x = r and y = s
(b) s-r flip-flop with inputs x = s and y = r
(c) j-k flip-flop with inputs x=j and y=k
(d) j-k flip-flop with inputs x=k and t=j

For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0. assume gate delays to be negligible

Which of the following statements is true ?
(a) Q goes to 1 at the CLK transition and stays at 1
(b) Q goes to 0 at the CLK transition and stays at 0
(c) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1
(d) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

In the circuit in figure S₂ to S₀ are select lines and X₇ and X₀ are input lines. S₀ and X_O are the LSBs. the output is

(a) indeterminate
(b) A . B
(c) A . B
(d) C . (A * B) + C . (A * B)

The input signal V₁ shown in figure is applied to the flip-flop of figure when initially in 0 state. assume all timing constraints are satisfied. the output Q is
The input signal V_Ishown in figure is applied to a flip-flop of figure when initially in its 0-state. assume all timing constraints are satisfied. the output Q is
For each of the positive edge-triggered j-k flip-flop used in the following figure, the propagation delay is T

Which of the following waveforms correctly represents the output at Q₁?

The circuit diagram of a standard TTL NOT gate is shown in the figure. when V_I = 2.5 V, the modes of operation of the transistors will be

(a) Q₁ : reverse active Q₂ : normal active; Q₃ : saturation ; Q₄ cut-off
(b) Q₁ : Reverse active Q₂ : saturation; Q₃ : saturation; Q₄ : cut-off
(c) Q₁ : saturation; Q₂ : Saturation; Q₃ : cut-off Q₄ : saturation
(d) Q₁ : saturation: Q₂ : Saturation ; Q₃ : saturation; Q₄ : normal active

The full scale output of a 10-bit DAC is 5 V. the resolution is

(a) 5 mV
(b) 10 mV
(c) 2.5 mV
(d) 20 mV

For the circuit shown in figure below, two 4-bit prallel-in serial-out shift registers loaded with the data shown are used to feed the data to a full adder. initially, all the flip-flop are in clear state, after applying two clock pulese, the outputs of the full-adder should be

(a) S = 0, C₀ = 0
(b) S = 0, C₀ = 1
(c) S = 1, C₀ = 0
(d) S = 1, C₀ = 1

The circuit shown in figure implements the functon

(a) (A + B) C + D
(b) (AB + C) D
(c) ( A + B) C + D
(d) (AB + C) D

Below circuit of gate in (RTL) resistor transistor logic family. the circuit represents

(a) NAND
(b) AND
(c) NOR
(d) OR

The full scale output of a DAC is 10 ma. if resolution is to be less than 40 uA, then required bits are

(a) 11
(b) 10
(c) 8
(d) 9

A particular 6-bit DAc has full-scale output rated at 1.260 v. its accuracy is specified as +0.11% of full scale and it has an offset error of +1 mv. the measurement that is not within the DAC specification, is

Input code                                       output
(a) 0 0 0 0 1 0                                               41.5 mV
(b) 0 0 0 1 1 1                                               140.2 mV
(c) 0 0 1 1 0 0                                                   242.5 mV
(d) 1 1 1 1 1 1                                                    1.25 V

Match list I and II find the correct answer using the codes given below the lists.

List I List II

BCD to 7-segment decoder 1. sequential circuit
4 to 1 MUX 2. combination circuit
4-bit shift register 3. neither sequential nor combinational circuit

Codes
P             Q                R                 S
(a)          2               1                 2                1
(b)          3                 2               1                 3
(c)            2               2                 1                1
(d)            3               1                  2                3

minimum number of NAND gate required to implement A (A + B) ( A + B + C) is equal to

(a) 3
(b) 4
(c) 5
(d) none of these

For a digital to analog conversion, the bit pattern is 10110

The correct flowing in R_F branch is
(a) V/22R
(b) V/66R
(c) V/44R
(d) None of these
Unit Exercise -2

Equation [X + Z(Y + (Z + XY)][X + Z(X + Y)] = 1
Putting X = 1 and X = 0
[1 + Z( X + (Z + Y)][0 + Z(1 + Y)] = 1
(1) (Z) = 1
Z = 1
Z = 0

contents 2-4-2-1 BCD number.

as j-k input to all flip-flop made high. the given counter is mode 10.
hence, frequency of output signal
= 10/10 = 1 kHz

Thus, the given CMOS gate satisfies the function of a negative NAND gate.

As MSB is 1 the number in negative. taking 2’s complement of the given number

Writing the expression in canonical form,
AC + BC = AC(B + B) + (A + A) BC
= ABC + ABC + ABC + ABC

F = A + AB + ABC + ABC + ABC (D + DE)
= A + AB + AB(C + C(D + E))
= A + A (B + B(C + D + E) = A + B + C + D + E

this can be wrtten as
= RS(P + Q) + RSP + RSPQ + RSP
= SP + RSP + PQRS + QRS

The largest positive going spike
V_NL = V_IL(MIN) – V_OL(MAX)
= 1 – 0.1 = 0.9 V
The largest negative going spike
V_NH = V_OH(MIN) – V_IH(MIN)
= 4.9 – 3.5 = 1.4 V

in signed 2’s complement the MSB represent the signal
P = 11101101 = (-19)
Q = 11100110 = (-26)₁₀
P-Q = -19 – (-26) = (7)₁₀
(17)₁₀ = 00000111

F₁ = AB + AB
F₂ = A + B = A.B
X = F₁F₂
= (AB + AB) . AB
= AB

For LED to glow p = 0
both input to NAND gate = 1
if any switch is closed AND gate output will be low.
if both switch are open. OR gate output will be low.
hence, LED does not emit light irrespective of switch position.

if input signal E is low, output will not be low. so, it must be high.

C₃*C₂*C₁ = 110 which indicate position 6 in error
transmitted code 1001100.

Truth table
Y = A + AB
X = YC + YC = (AB + AB) C + (AB + AB)C
= ABC + ABC + ABC + ABC

This is a 5-bit synchronous counter. when the output of Q₃ and Q₄ is high then, the output of NAND gate is low. this will clear all flip-flops. so, it is a mod-24 counter.
When 11000 occur the CLR input is activated and all flip-flops are immediately cleared.

The timing diagram of modulo-6 ripple counter
i.e., in modulo-6 counter at 110 all state must be cleaned CB = 1.
C = B = 0 and output of 20 input gate is also 0.
hence, OR gate required 40 perform the decimal function.

in 2’s complement
A = 01000110
B = 11010011
A,B represents the 2’s complement of A and B respectively

The minimum number of 2 to 1 multiplexer required to realize 4 to 1 MUX is 3.

V_NH = V_OH(MIN) – V_IH(MIN)
V_IH(MIN) = V_OH(MIN) – V_NH
= – 0.8 – 0.5 = – 1.3 V
V_NL = V_IL(MAX) – V_OL(MAX)
V_IL(MAX) = V_NL+ V_OL(MAX)
= 0.5 + (-2)
= – 1.5 V

After t = t₁ – shift regist output e = 0110(6)
input of address line of ROM at 6; 1010 is stored.
At next rising edge of clock 1010 (10) the stored data in ROM 1000

F₁ = A + B
= A . B = A . B
Z = AB . B.C
= ABC

for 2 input AND gate,
Y = AB
Y = AB + AB

fall-out minimum – DTL (undesired)
power consumption is minimum – CMOS (Desired)
propagation delay is minimum – ECL – (Desried)

F₁ = AB
F₂ = (B + C)
Z = F₁.F₂
= (AB).(B + C)
= ABC

from truth table we can invite
f = ABC + ABC = B(AC + AC)
= B (A + C) (A + C)

F = I₀S₁S₀ + I₁S₁S₀ + I₂S₁S₀ + I₃S₁S₀
I₀ = C
I₁ = D
I₂ = C
I₃ = C .D
S₁ = A
S₀ = B
F (A, B, C, D) = ABC + ABD + ABC + ABC D
= ABC (D + D) + AB (C + C) D + ABC (D + D) + ABC D
= ABCD + ABC D + ABCD + ABCD + ABCD + ABC D + ABC D
= M (2, 3, 5, 7, 8, 9, 12)

The truth table
D₀ = Q₁
D₁ = Q₀
Hence, the inputs D₀ and D₁ should be connected to Q₁ and Q₀ respectively.

the simpiified diagram
we can write
V_A = 1/8 + 1/2 = 5/8
V_A = V₈ = 5/8 V
KVL at node B,
0 – 5/8 5/8 – V₀
8/1K = 8/7K
V₀ = 5 V

Y = RS + PR + PQ + PQ
= RS + (PR . PQ . PQ)
= RS + (P + R) (P + Q) (P + Q)
= RS + (P + PR + PQ + RQ) (P + Q)
= RS + (PRQ + PQ + PQR + PQ + QR) [PP = 0]
= RS + PQ + QR (P + P + 1)
= RS + PQ + QR
= R + S + PQ + PQR + PQS
By simplifing
Z = R + S + PQ + PR + PQS + QRS
= R (1 + P + QS)+ S (1 + PQ) + PQ
= R + S + PQ
We can write
W = Z and X = Z

F = BD + BCD + ABD

As shown in figure.
the select line for chip # 1 is A₈ + A₉.
The select line for chip # 2 is A₈ + A₉. Hence, the memory address range F800 – F9FF is not represented by chip # 1 and chip #2.

we can write
V₀ = – V₁ (R/R B₀ + R/2R B₁ + R/4R B₂ + R/8R B₃)
For V₁ = 5 V,
V₀ = – 5 (1 + 1/2 + 1/4 + 1/8)
= – 9.375 V
With maximum tolerance 10% in voltage and 5% inresistors
V_O = – 5.5 (110/90 x 110/2×90 + 110/4×90 + 110/8×90
= – 12.604
tolerance = 12.604 – 9.375/9.375 x 100 = 34.44%

Y = ABCD + ABCD + ABCD + ABC D
= ABCD + ABC D + BCD (A + A)
= ABCD + ABC D + BCD

f = AC + BC
= AC (B + B) + BC (A + A) (B + B) = 1
= ABC + ABC + ABC + ABC

after t = t₁ at the first rising edge of clock, the output of shift register is 0110, which is input to address line of ROM, at 0110 (6) data 1010 is stored which will be on bus. at next rising edge of clock 1010 is applied to register. so, at this time data stored in ROM at 1010 (10), 1000 will be on bus.

As circuit has one stable state and require external triggering to change state. so, it represnts a multistable multivibrator.

Boolean expression
= (X + Y)(X + Y) (X + Y)
= (X + XY + XY) (X + Y)
= XY + XY
= XY

let the output from the upper first level multiplexer and from the lower first level multiplexer is f₂.
f₁ = wx + wx
f₂ = wx + wx = x(w + w) = x
f = f₁yz + f₂yz + yz
= (wx + wx) yz + xyz + yz
f = wxyz + wx yz + xy + yz

here, 101 repeat itselt after every two cycles. the output Q₂Q₁Q₀ will be
= f_c/2

hence, e(Q₁Q₂) sequence
11, 10, 00, 11, 10

width of one pulse = 1/10 x 10⁶
= 0.1 us
width for 1 V = 10 us
for 10 V = 10 x 10
so, corresponding pulse count = 100/0.1 = 1000

Z = A + (AB + BC) + C
= A + (A + B + B + C) + C
= A + B + C
and AB + BC + CA = A + B + B + C + C + A = A + B + C

I₀ = 0
I₁ = y + z
I₃ = yz + yz = y . z
I₂ = z

in ripple counter clock will propagate through each flip-flop. hence worst case delay in ripple counter = 4 x 10 ms = 40 ms.
in synchronous counter clock will be given simultaneously to all flip-flops. hence, worst case delay will be = 10 ms.

for the circuit
step size = R_F/8K x 5
0.5 = R_F/8K x 5
R_F = 800

when P stuck at 1. the x will be 1 whatever be other input B and C. hence, the output f as shown above is A.

F₁ = abc + abc + bc = ac + ab
F₂ = abc + ab + abc = ac + be
F₃ = abc + abc + ac = ab + bc
thus, P₁ = ab, p₂ = ac, p₃ = bc, p₄ = bc, p₅ = ab

the given ripple counter is positive edge triggered flip-flop. hence, at every clock Q₂ Q₁ Q₀ will be changed. the present state is 011, the next state will be 100.

for a 4-bit modulo-6 counter
number of flip-flops = 4
total delay = 4 x 50 us = 200 x 10^-9
so, maximum frequency = 1/200 x 10^-9
= 5 MHz

step size = 9.99/999 = 10 mV
input code = 0110 1001 0101₂
= 695₁₀
so, output voltage V_OUT will be
V_OUT = 695 x 10
= 6950 mV
= 69.5 V

D_O = A₁A₀, D₁ = A₁A₀, D₂ = A₁A₀
For output f
for first decoder A₀ = x, A₁ = Y, D₂ = YX, D₃ = XY
For second decoder A₁ = D₂D₃ = YXXY = 0, A₀ = Z
F = D₀ + D₁ + A₁A₀ + A₁A₀ = A₁ = 1

for a 4-bit ripple counter
R = Delay = 4 x 10
= 40 us
for a synchronous 4-bit counter
S = Delay = 10 ns
Q₁Q₂ = 00, 01, 10, 00, 01……..

fan-out (low) = I_OL(MAX)/I_IL(MAX) = 8/0.1 = 80
Fan-out (high) = I_OH(MAX)/I_IH(MAX) = 400/20 = 20
The fan-out is chosen the smaller of the two. so, the fan-out will be 20.

fan NAND gate in any one input is zero, then its output will be 1. so if p₁ is zero the Q₁ becomes 1. now we can calculate Q₂ because its both inputs are 1, so Q₂ will be zero. by using these values of Q₁ and Q₂ as feedback with new input new value of Q₁ and Q₂ can be calculated.

output Z,
Z = S₀S₁. 1 + S₀S₁.1 + S₀S₁.1 + S₀S₁C
Put S₀ = A and S₁ = B,
Z = AB + AB + AB + ABC
= ABC + ABC + AB + AB + ABC

the j-k truth table,
hence, Q_N+1 will be 1.

after three clock pulses the flip-flops are cleared. thus the circuit represents the MOD-3 counter.

if A = – V_DD then M₁ is on and Y = 0 V
If B = C = – V_DD and A = 0, then M₃ and M₂ are on but M₁ is off hence Y = 0 V.
If B = C = 0 then M₁ is off and either or both M₂ and M₃ will be off, which implies on current flowing through M₄ hence, Y = – V_DD
Thus, given circuit satisfies the logic equation A + BC.

the truth table
we can write
f = xY + xy + xy
= x (y + y) + xy
= x + xy
= x + y
the circuit realization
hence, one NOR and one OR gate are required As each having one unit cost. hence, the minimum cost required is 2 unit.

here in the circuit no active loop in the network because variable b interrupts the loop t two different points.
when b = 1
Z₁ = Z₀d, Z₀ = e + c
when b = 0,
Z₁ = ad, Z₀ = ad + c
thus, there is no feedback of signals in the physical loop and the circuit is combinational.

for each successive gate, that has a transistor in saturation, the current required is
I_B(SAT) + I_C(SAT)/B = V_CC – V_CE(SAT)/BR_C = 5 – 0.2/50(640)
= 0.15 mA
For n attached gate I₀ = nI_B(SAT)
to assure no logic error V₀ = V_CC – I_OR_C > V_H = 3.5 V
n < V_{CC –}3.5/R_CI_B(SAT) = 5 – 3.5 /640 (0.15) = 15.6
n < 15

this is a 1-bit subtract or with R as borrow.
Y = P * Q * R
Z = RQ + PR + QP
Hence, perform P-Q operation.

let initial state is 000,
because 0 state of previous flip-flops changes the state of next so it is a down counter.

lnitially let us consider at t = 0, the voltage across capacitor V_C = V(0) and V₀ = V(1), the output V_O will charge capacitor C with the time constant t = RC. when V_C reaches to V(1) the output of inverter goes to V(0) and the capacitor starts discharging thus, the square waveform will be generated at the output.

Z = D (ABC + ABC + ABC + ABC + ABC)
= D(AB(C + C) + BC (A + A) + ABC)
= D(AB + BC + ABC) = D(B(A + AC) + BC)
= D (BA + BC + BC) = D (B . C + AB)

the timing diagram

if all inputs A, B, C are high, then
input to inverter low
output Y = High
if all the inputs A, B, and C are low, then
input to inverter = low
output Y = high
thus Y = ABC + ABC = ABC + (A + B + C)

the truth table for given D flip-flop
Z = XQ + YQ
The equation of J-K flip-flop
Q_N+1 = JQ_N + KQ
X = K and Y = J

the flip-flop shown in the circuit is a negative edge triggered T flip-flop. so, at the negative edge of the clock V_I flip-flop will invert the output, if there is 1 at input.

(a)
(b) given clock pulse
(a)
(a)

resolution = V_FS/2^N – 1
= 5/2¹⁰ – 1 = 5/1024 – 1 = 5/1023 = 5 mV

after applying 1 st CLK PUBE,
A – 1
B – 0
C – 0
S – 0
C_O – 1
After applying 2nd CLK PUBE,
A – 1
B – 1
C – 1
S – 1
C₀ – 1

the operation of circuit is given below.
from the table, output can be summarized as
Y = (A + B) C + D

(i) V₁ = 0 and V₂ = 0 Q₁ = Q₂= off
V_B = V_CE. = V_CE2 = V_CC
Q₃ = On, V₀ = 0
(ii) V₁ = 0 and V₂ = 1
Q₁ = off, Q₂ = On, V_B = Q₃ = off
or V₀ = 1
(iii) V₁ = 1 and V₂ = 0
Q₁ = On , Q₂ = Off V_B = V_CE2
Q₃ = Off V₀ = 1
(iv) V₁ = 1 and V₂ = 1
Q₁ = Q₂= on, V_B = 0
Q₃ = Off
V_O = V_CE3 Or V₀ = 1
V₀ = V₁ + V₂

resolution = 40 uA
the step required = 10 m/40 u = 250
therefore, it required 8-bit.

step size = 9.99/999 = 10 mV
0110 1001 0101
6 9 5
695 x 10 m = 6.95 v
(c) step size = 1.26/63 = 20 mV
+ 0.1%F.3 = + 1.26 V
Maximum total error = + 1.26 + 1 = 2.26 mV
000010₂ = 2 x 20 m = 40 mV
(41.5 mV is within specs.)
000111₂ = 7 x 20 m = 140 mV
(140.2 mV is within specs.)
001100₂ = 12 x 20 m = 240 mV
(242.5 mV isn’t within specs.)
11111₂ = 63 x 20 m = 1.26 v
(1.258 is within specs.)

F = A (A + B) (A + B + C)
= (A + AB) (A + B + C)
= A + AB + AC + AB + AB + ABC
= A (1 + B + C + B + B + BC)
= A
So, there is no need of NAND gate

in the modulo 6 ripple counter shown in the figure the output of the 2 input | given figure 2 works as a

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