DigitalLogicDesign
Question 1 
bias of 127.
S : 1 E : 10000001 F : 11110000000000000000000
Here S, E and F denote the sign, exponent and fraction components of the floating point representation.
The decimal value corresponding to the above representation (rounded to 2 decimal places) is _______
A  7.75 
Sign bit S= 1. The given number is a negative number.
Biased Exponent E = 2^{7} + 1= 129
Actual Exponent e = E127
= 129 127
= 2
The decimal value= (1)^{s} x 1.M x 2^{e}
= (1) 1 x 1.1111 x 2^{2}
=  (111.11)
=  (7 + 0.75)
= 7.7
Question 2 
A  21 
B  528

C  D2 
D  15 
On converting (210)3 in decimal, we will get:=>
2*3^{2}+1*3=2*9+3=21_{10 }
=>(15)_{16}
Question 3 
A  
B  
C  
D 
XY’+Z’ is a minimal SoP expression which represents the function (X,Y,Z).
The expression XY’ + YZ’ + X’Y’Z’ can be reduced to XY’+Z’
XY’ + YZ’ + X’Y’Z
= Y’(X+X’Z’) + YZ
= Y’(X+Z’) + Y
= XY’ + Y’Z’ + YZ’
= XY’ + (Y’+Y)Z’
= XY’ + Z’.
The expression (X+Z’)(Y’+Z’) is a PoS expression which also represents the same function (X,Y,Z).
Question 4 
Which one of the following choices gives the correct values of x and y?
A  x is 1 and y is 1 
B  x is 0 and y is 1 
C  x is 1 and y is 0 
D  x is 0 and y is 0 
C2 checks the bits d1, d3, d4, d6, d7.
C2=1, d1= 1, d3= 1, d4= 0, d6= 0, d7= 1.
The number of 1s is even. So, even parity is used in this problem.
C1 checks the bits d1, d2, d4, d5, d7.
C1=0, d1= 1, d2= 0, d4= 0, d5= x, d7= 1.
As the parity used is even parity, the value of d5 should be 0.
x=d5=0
C8 checks the bitsa d5, d6, d7, d8.
C8=y, d5= x=0, d6= 0, d7= 1, d8= 1.
As the parity used is even parity, the value of C8 should be 0.
C8=y=0.
x=y=0.
Question 5 
A  011, 101, 000 
B  001, 010, 111 
C  001, 010, 000 
D  011, 101, 111 
The truth table will be
RQP 
Rn Qn Pn 
000 
011 
011 
101 
101 
000 
Therefore, the next three states are : 101, 000 and 011
Question 6 
The logic expression for the output of the circuit shown in figure below is:
A  
B  
C  
D  
E  None of the above. 
Question 7 
The number of flipflops required to construct a binary modulo N counter is __________.
A  ⌈log_{2} N⌉ 
Question 8 
Consider nbit (including sign bit) 2’s complement representation of integer number. The range of integer values, N, that can be represented is _________ ≤ N ≤ _________
A  2^{n1} to 2^{n1}  1 
Question 9 
Following 7 bit single error correcting Hamming coded message is received. (figure below):
Determine if the message is correct (assuming that at most 1 bit could be corrupted). If the message contains an error find the bit which is erroneous and gives the correct message.
A  Theory Explanation. 
Question 10 
Write a program in 8085 Assembly language to Add two 16bit unsigned BCD(8421 Binary Coded Decimal) number. Assume the two input operands are in BC and DE Register pairs. The result should be placed in the register pair BC. (Higher order register in the register pair contains higher order digits of operand)
A  Theory Explanation. 
Question 11 
Find the contents of the flipflop Q_{2}, Q_{1} and Q_{0} in the circuit of figure, after giving four clock pulses to the clock terminal. Assume Q_{2}Q_{1}Q_{0} = 000 initially.
A  Theory Explanation. 
Question 12 
(a) Assume that a CPU has only two registers R_{1} and R_{2} and that only the following instruction is available XOR R_{i}, R_{j}; {R_{j} ← R_{i} ⊕ R_{j}, for i,j = 1,2}
Using this XOR instruction, find an instruction sequence in order to exchange
the contents of the registers R_{1} and R_{2}.
(b) The line p of the circuit shown in figure has stuck at 1 fault. Determine an input test to detect the fault.
A  Theory Explanation. 
Question 13 
What values of A, B, C and D satisfy the following simultaneous Boolean equations?
A  A = 1, B = 0, C = 0, D = 1 
B  A = 1, B = 1, C = 0, D = 0 
C  A = 1, B = 0, C = 1, D = 1 
D  A = 1, B = 0, C = 0, D = 0 
Question 14 
The number of 1’s in the binary representation of
(3*4096 + 15*256 + 5*16 + 3) are:
A  8 
B  8 
C  10 
D  12 
= (11000000000000)_{2}
15 × 256 = 15 × 2^{8}
= (111100000000)_{2}
5 × 16 = 5 × 2^{4}
= (1010000)_{2}
3 = (11)_{2}
Hence, all binary numbers,
∴ 101's
Question 15 
(a) Implement a circuit having the following output expression using an inverter and NAND gate .
(b) What is the equivalent minimal Boolean expression (in sum of products form)
for the Karnaugh map given below?
A  Theory Explanation. 
Question 16 
(a) An asynchronous serial communication controller that uses a start stop scheme for controlling the serial I/O of a system is programmed for a string of length seven bits, one parity bit (odd parity) and one step bit. The
transmission rate is 1200 bits/second.
(i) What is the complete bit stream that is transmitted for the string ‘0110101’?
(ii) How many such strings can be transmitted per second?
(b) Consider a CRT display that has a text mode display format of 80 × 25 characters with a 9 × 12 character cell. What is the size of the video buffer RAM for the display to be used in monochrome (1 bit per pixel) graphics mode?
A  Theory Explanation. 
Question 17 
A multiplexer is placed between a group of 32 registers and an accumulator to regulate data movement such that at any given point in time the content of only one register will move to the accumulator. The minimum number of select lines needed for the multiplexer is _____.
A  5 
A 2^{5}x1 Multiplexer with 5 select lines selects one of the 32(= 2^{5}) registers at a time depending on the selection input.
The content from the selected register will be transferred through the output line to the Accumulator.
Question 18 
If there are m input lines and n output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of m + n is ____.
A  1034 
Each output line of the decoder is connected to one of the 1K(= 1024) rows of RAM.
Each row stores 1 Byte.
m=10 and n=1024
Question 19 
Consider the Boolean function z(a,b,c).
Which one of the following minterm lists represents the circuit given above?
A  Z = ∑(0,1,3,7) 
B  Z = ∑(2,4,5,6,7) 
C  Z = ∑(1,4,5,6,7) 
D  Z = ∑(2,3,5) 
Convert a+b’c into canonical form which is sum of minterms.
a + b’c = a(b + b’)(c + c’) + (a + a’)b’c
= abc + abc’ + ab’c + ab’c’ + ab’c + a’b’c
= Σ(7,6,5,4,1)
Question 20 
Consider three registers R1, R2 and R3 that store numbers in IEEE754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x42200000 and 0xC1200000, respectively.
If R3 = R1/R2, what is the value stored in R3?
A  0x40800000 
B  0x83400000 
C  0xC8500000 
D  0xC0800000 
R1 = 1.0100..0 X 2^{132127}
= 1.0100..0 X 2^{5}
= 101.0 X 2^{3}
= 5 X 8
= 40
R2 = (1) x 1.0100..0 X 2^{130127}
= (1) x 1.0100..0 X 2^{3}
= (1) x 101.0 X 2^{1}
= (1) x5 X 2
= 10
R3 = R1/R2
= 4
= (1)x 1.0 x 2^{2}
Sign = 1
Mantissa = 000..0
Exponent = 2+127 = 129
R3 = 1100 0000 1000 000..0
= 0x C 0 8 0 0 0 0 0
Question 21 
The truth table
represents the Boolean function
A  X 
B  X + Y 
C  X ⊕ Y 
D  Y 
Question 22 
The decimal value 0.5 in IEEE single precision floating point representation has
A  fraction bits of 000…000 and exponent value of 0 
B  fraction bits of 000…000 and exponent value of −1 
C  fraction bits of 100…000 and exponent value of 0 
D  no exact representation 
So, value of the exponent = 1
and
fraction is 000…000 (Implicit representation)
Question 23 
The amount of ROM needed to implement a 4 bit multiplier is
A  64 bits 
B  128 bits 
C  1 Kbits 
D  2 Kbits 
Hence option D is the answer.
Question 24 
What is the minimal form of the karnaugh map shown below? Assume that X denotes a don't care term
A  
B  
C  
D 
Question 25 
A ROM is sued to store the table for multiplication of two 8bit unsigned integers. The size of ROM required is
A  256 × 16 
B  64 K × 8 
C  4 K × 16 
D  64 K × 16 
No. of results possible = 2^{8} × 2^{8} = 2^{16} = 64K
Then total size of ROM = 64K × 16
Question 26 
Both’s algorithm for integer multiplication gives worst performance when the multiplier pattern is
A  101010 …..1010 
B  100000 …..0001 
C  111111 …..1111 
D  011111 …..1110 
Question 27 
Consider the following floating point number representation
The exponent is in 2's complement representation and mantissa is in the sign magnitude representation. The range of the magnitude of the normalized numbers in this representation is
A  0 to 1 
B  0.5 to 1 
C  2^{23} to 0.5 
D  0.5 to (12^{23}) 
Question 28 
Consider the circuit given below which has a four bit binary number b_{3}b_{2}b_{1}b_{0} as input and a five bit binary number d_{4}d_{3}d_{2}d_{1}d_{0} as output. The circuit implements:
A  Binary of Hex conversion

B  Binary to BCD conversion 
C  Binary to grey code conversion 
D  Binary to radix12 conversion 
Whenever, b_{2} = b_{3} = 1, then only 0100, i.e., 4 is added to the given binary number. Lets write all possibilities for b.
Note that the last 4 combinations leads to b_{3} and b_{2} as 1. So, in these combinations only 0010 will be added.
1100 is 12
1101 is 13
1110 is 14
1111 is 15
in binary unsigned number system.
1100 + 0100 = 10000
1101 + 0100 = 10001, and so on.
This is conversion to radix 12.
Question 29 
Consider the circuit in below figure. f implements
A  
B  A + B + C 
C  A ⊕ B ⊕ C 
D  AB + BC + CA 
Question 30 
What is the equivalent Boolean expression in productofsums form for the Karnaugh map given below.
A  
B  
C  
D  
E  None of the above 
Question 31 
A logic network has two data inputs A and B, and two control inputs C_{0} and C_{1}. It implements the function F according to the following table.
Implement the circuit using one 4 to 1 Multiplexer, one 2input Exclusive OR gate, one 2input AND gate, one 2input OR gate and one Inverter.
A  Theory Explanation. 
Question 32 
Consider the synchronous sequential circuit in the below figure.
(a) Draw a state diagram, which is implemented by the circuit. Use the following names for the states corresponding to the values of flipflops as given below.
(b) Given that the initial state of the circuit is S_{4}, identify the set of states, which are not reachable.
A  Theory Explanation. 
Question 33 
Let * be defined as x * y = x' + y. Let z = x * y. Value of z * x is
A  x'+y 
B  x 
C  0 
D  1 
Question 34 
An Nbit carry look ahead adder, where N is a multiple of 4, employs ICs 74181 (4 bit ALU) and 74182 (4 bit carry look ahead generator).
The minimum addition time using the best architecture for this adder is
A  proportional to N 
B  proportional to log N 
C  a constant 
D  None of the above 
Question 35 
Let f(x, y, z) = x' + y'x + xz be a switching function. Which one of the following is valid?
A  
B  xz is a minterm of f 
C  xz is an implicant of f 
D  y is a prime implicant of f 
Question 36 
Given √224)_{r} = 13)_{r}.
The value of the radix r is:
A  10 
B  8 
C  5 
D  6 
Convert r base to decimal.
√2r^{2} + 25 + 4 = r + 3
Take square both sides,
2r^{2} + 2r + 4 = r^{2} + 6r + 9
r^{2}  4r  5 = 0
r^{2}  5r + r  5 = 0
r(r  5) + (r  5) = 0
r = 1, 5
r cannot be 1,
So r = 5 is correct answer.
Question 37 
Consider a logic circuit shown in figure below. The functions f_{1}, f_{2} and f (in canonical sum of products form in decimal notation) are:
f_{1}(w,x,y,z) = ∑8,9,10 f_{2}(w,x,y,z) = ∑7,8,12,13,14,15 f(w,x,y,z) = ∑8,9
The function f_{3} is
A  Σ9,10 
B  Σ9 
C  Σ1,8,9 
D  Σ8,10,15 
Since, f_{1} and f_{2} are in canonical sum of products form, f_{1}⋅f_{2} will only contain their common terms that is f_{1}⋅f_{2} = Σ8.
Now,
Σ8 + f_{3} = Σ8,9
So, f_{3}= Σ9
Question 38 
What happens when a bitstring is XORed with itself ntimes as shown:
[B⊕(B⊕(B⊕(B........ n times)]
A  complements when n is even 
B  complements when n is odd 
C  divides by 2^{n} always 
D  remains unchanged when n is even 
Consider:
B⊕(B⊕B)
= B⊕0
= 0 (if consider n times it remains unchanged)
Question 39 
A multiplexor with a 4 bit data select input is a
A  4:1 multiplexor 
B  2:1 multiplexor 
C  16:1 multiplexor 
D  8:1 multiplexor 
For 4 bit data it selects 2^{4} : 1 = 16: 1 input
Question 40 
The threshold level for logic 1 in the TTL family is
A  any voltage above 2.5 V 
B  any voltage between 0.8 V and 5.0 V 
C  any voltage below 5.0 V 
D  any voltage below V_{cc} but above 2.8 V 
Question 41 
The octal representation of an integer is (342)_{8}. If this were to be treated as an eightbit integer is an 8085 based computer, its decimal equivalent is
A  226 
B  98 
C  76 
D  30 
If this can be treated as 8 bit integer, then the first becomes sign bit i.e., '1' then the number is negative.
8085 uses 2's complement then
⇒ 30
Question 42 
The function represented by the Karnaugh map given below is:
A  A⋅B 
B  AB+BC+CA 
C  
D  None of the above 
Question 43 
Which of the following operations is commutative but not associative?
A  AND 
B  OR 
C  NAND 
D  EXOR 
Question 44 
Suppose the domain set of an attribute consists of signed four digit numbers. What is the percentage of reduction in storage space of this attribute if it is stored as an integer rather than in character form?
A  80% 
B  20% 
C  60% 
D  40% 
We have four digits. So to represent signed 4 digit numbers we need 5 bytes, 4 bytes for four digits and 1 for the sign.
So required memory = 5 bytes.
Now, if we use integer, the largest no. needed to represent is 9999 and this requires 2 bytes of memory for signed representation.
9999 in binary requires 14 bits. So, 2 bits remaining and 1 we can use for sign bit.
So, memory savings,
= 5  2/5 × 100
= 60%
Question 45 
(a) The implication gate shown below, has two inputs (x and y), the output is 1 except when x=1 and y=0. Realize f = x'y + xy' using only four implication gates.
(b) Show that the implication gate is functionally complete.
A  Theory Explanation. 
Question 46 
Design a synchronous counter to go through the following states:
1, 4, 2, 3, 1, 4, 2, 3, 1, 4,...........
A  Theory Explanation. 
Question 47 
?
A  x NAND X 
B  x NOR x 
C  x NAND 1 
D  x NOR 1 
Question 48 
A  
B  
C  
D 
⇒ CD+AD = D(A+C)
Question 49 
Booth’s coding in 8 bits for the decimal number –57 is
A  0 – 100 + 1000 
B  0 – 100 + 100  1 
C  0 – 1 + 100 – 10 + 1 
D  00 – 10 + 100  1 
Question 50 
The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit number is
A  On^{2} 
B  O(n) 
C  O(log n) 
D  O(1) 
Total delay = 1 * 2n  1 = O(2n  1) = n