Digital Logic Design

Previous Job QnS (Digital Logic Design)

Topic Wise Question Bank

- ☆
  1
  Digital Logic DesignUniversal Gate
  Draw the circuit schematic diagrams to build an Exclusive-OR (XOR) logic function using only universal NAND gates.
  CB, O(IT-24), 26 | Officer (IT)
  XOR gate: (Using 4 NAND Gates)
  [ Previous Buet Pattern Question]
- ☆
  2
  Digital Logic DesignUniversal Gate
  What is a Universal Gate? Prove that the NAND Gate is a Universal Gate.
  Combined Bank, AP-22, 26 | Assistant Programmer
  
  Universal Gate
  A Universal Gate is a logic gate that can be used to implement any Boolean function (i.e., any logic circuit). If we can build the basic gates NOT, AND, and OR using only one type of gate, then that gate is called a universal gate.
  Proof: NAND is a Universal Gate
  To prove NAND is universal, we show that we can construct NOT, AND, and OR using only NAND gates.
  Since we can build NOT, AND, and OR using only NAND gates, we can build any Boolean expression. Therefore, the NAND gate is a Universal Gate.
  
  Universal Gate
  Universal Gate হলো এমন একটি logic gate যার সাহায্যে যেকোনো Boolean function বা যেকোনো logic circuit তৈরি করা যায়। যদি একটি মাত্র gate ব্যবহার করে NOT, AND, এবং OR gate তৈরি করা যায়, তাহলে সেই gate কে universal gate বলা হয়।
  প্রমাণ: NAND Gate Universal Gate
  NAND universal প্রমাণ করতে হলে দেখাতে হবে যে শুধুমাত্র NAND gate দিয়ে NOT, AND, এবং OR তৈরি করা যায়।
  কারণ শুধুমাত্র NAND gate ব্যবহার করে NOT, AND, এবং OR তৈরি করা যায়, তাই যেকোনো Boolean function তৈরি করা সম্ভব। সুতরাং NAND gate একটি Universal Gate।
- ☆
  3
  Digital Logic DesignUniversal Gate
  Explain how any Boolean function can be implemented using only universal gates.
  Combined Bank, O(IT-23), 26 | Officer (IT)
  Universal gates are logic gates that can implement any Boolean function without using any other type of gate.
  The two universal gates are:
  - NAND Gate
  - NOR Gate
  Using only NAND gates or only NOR gates, all basic logic gates such as AND, OR, and NOT can be constructed. Since any Boolean function is built using these basic gates, any Boolean function can also be implemented using universal gates.
  Implementation Using NAND Gate
  1. NOT Gate using NAND
  When both inputs of a NAND gate are connected together:
  $$
  Y=\overline{A\cdot A}=\overline{A}
  $$
  2. AND Gate using NAND
  First NAND operation gives:
```
(A · B)'
```
  Applying another NAND as NOT operation:
  $$
  Y=\overline{\overline{A\cdot B}}=A\cdot B
  $$
  3. OR Gate using NAND
  Using De Morgan’s theorem:
  $$
  A+B=\overline{\overline{A}\cdot\overline{B}}
  $$
  So OR gate can also be implemented using only NAND gates.
  Implementation Using NOR Gate
  1. NOT Gate using NOR
  When both inputs are same:
  $$
  Y=\overline{A+A}=\overline{A}
  $$
  2. OR Gate using NOR
  First NOR operation gives:
```
(A + B)'
```
  Applying another NOR as NOT operation:
  $$
  Y=\overline{\overline{A+B}}=A+B
  $$
  3. AND Gate using NOR
  Using De Morgan’s theorem:
  $$
  A\cdot B=\overline{\overline{A}+\overline{B}}
  $$
  Since NAND and NOR gates can create all basic logic gates, and all Boolean functions are formed using basic gates, any Boolean function can be implemented using only NAND gates or only NOR gates.
  Universal gate হলো এমন logic gate যা অন্য কোনো gate ব্যবহার না করে যেকোনো Boolean function বাস্তবায়ন করতে পারে।
  দুটি universal gate হলো:
  - NAND Gate
  - NOR Gate
  শুধুমাত্র NAND gate বা শুধুমাত্র NOR gate ব্যবহার করে AND, OR এবং NOT-এর মতো সব basic logic gate তৈরি করা যায়। আর যেহেতু সব Boolean function এই basic gate ব্যবহার করে তৈরি হয়, তাই যেকোনো Boolean function universal gate ব্যবহার করে বাস্তবায়ন করা সম্ভব।
  NAND Gate ব্যবহার করে বাস্তবায়ন
  1. NAND দিয়ে NOT Gate
  যখন NAND gate-এর দুই input একসাথে যুক্ত করা হয়:
  $$
  Y=\overline{A\cdot A}=\overline{A}
  $$
  2. NAND দিয়ে AND Gate
  প্রথম NAND operation দেয়:
```
(A · B)'
```
  আবার NAND ব্যবহার করে NOT operation করলে:
  $$
  Y=\overline{\overline{A\cdot B}}=A\cdot B
  $$
  3. NAND দিয়ে OR Gate
  De Morgan’s theorem অনুযায়ী:
  $$
  A+B=\overline{\overline{A}\cdot\overline{B}}
  $$
  অতএব শুধুমাত্র NAND gate ব্যবহার করেও OR gate তৈরি করা যায়।
  NOR Gate ব্যবহার করে বাস্তবায়ন
  1. NOR দিয়ে NOT Gate
  যখন দুই input একই হয়:
  $$
  Y=\overline{A+A}=\overline{A}
  $$
  2. NOR দিয়ে OR Gate
  প্রথম NOR operation দেয়:
```
(A + B)'
```
  আবার NOR ব্যবহার করে NOT operation করলে:
  $$
  Y=\overline{\overline{A+B}}=A+B
  $$
  3. NOR দিয়ে AND Gate
  De Morgan’s theorem অনুযায়ী:
  $$
  A\cdot B=\overline{\overline{A}+\overline{B}}
  $$
  যেহেতু NAND এবং NOR gate ব্যবহার করে সব basic logic gate তৈরি করা যায়, এবং সব Boolean function basic gate দিয়ে তৈরি হয়, তাই শুধুমাত্র NAND gate বা শুধুমাত্র NOR gate ব্যবহার করে যেকোনো Boolean function বাস্তবায়ন করা সম্ভব।

☆

Digital Logic DesignMultiplexer/Demultiplexer

What is the difference between a Multiplexer and a Demultiplexer? Explain one practical application of each in digital systems.

CB, O(IT-24), 26 | Officer (IT)

Difference Between Multiplexer (MUX) and Demultiplexer (DEMUX)

Multiplexer (MUX)	Demultiplexer (DEMUX)
A Multiplexer (MUX) is a digital circuit that selects one input from multiple input lines and forwards it to a single output line.	A Demultiplexer (DEMUX) is a digital circuit that receives data from one input line and routes it to one of multiple output lines.
Many Inputs → One Output.	One Input → Many Outputs.
Uses Select Lines to choose one input.	Uses Select Lines to choose the destination output.
Acts as a Data Selector.	Acts as a Data Distributor.
Reduces the number of communication lines.	Distributes data to different devices or destinations.

Practical Applications

Multiplexer (MUX):
Used in Communication Systems to transmit multiple signals over a single communication channel, reducing wiring and transmission cost.

Demultiplexer (DEMUX):
Used at the receiving end of Communication Systems to separate the received data and deliver it to the correct output device or destination.

Conclusion

A Multiplexer combines multiple input signals into one output, whereas a Demultiplexer distributes one input signal to one of many outputs. They are widely used together in digital communication and data transmission systems.

Multiplexer (MUX) এবং Demultiplexer (DEMUX)-এর মধ্যে পার্থক্য

Multiplexer (MUX)	Demultiplexer (DEMUX)
Multiplexer (MUX) হলো একটি Digital Circuit, যা একাধিক Input Line থেকে একটি Input নির্বাচন করে একটি Output Line-এ পাঠায়।	Demultiplexer (DEMUX) হলো একটি Digital Circuit, যা একটি Input Line-এর Data-কে একাধিক Output Line-এর মধ্যে নির্দিষ্ট একটি Output-এ পাঠায়।
অনেক Input → একটি Output।	একটি Input → অনেক Output।
Select Line ব্যবহার করে Input নির্বাচন করে।	Select Line ব্যবহার করে কোন Output-এ Data যাবে তা নির্ধারণ করে।
Data Selector হিসেবে কাজ করে।	Data Distributor হিসেবে কাজ করে।
Communication Line-এর সংখ্যা কমাতে সাহায্য করে।	Data বিভিন্ন Device বা Destination-এ বিতরণ করতে ব্যবহৃত হয়।

ব্যবহারিক প্রয়োগ

Multiplexer (MUX):
Communication System-এ একাধিক Signal-কে একটি Communication Channel-এর মাধ্যমে প্রেরণের জন্য ব্যবহৃত হয়, ফলে Wiring এবং Transmission Cost কমে।

Demultiplexer (DEMUX):
Communication System-এর Receiver Side-এ প্রাপ্ত Data-কে সঠিক Device বা Output Line-এ বিতরণ করার জন্য ব্যবহৃত হয়।

উপসংহার

Multiplexer (MUX) একাধিক Input থেকে একটি Output নির্বাচন করে, আর Demultiplexer (DEMUX) একটি Input-কে একাধিক Output-এর মধ্যে নির্দিষ্ট একটিতে বিতরণ করে। Digital Communication এবং Data Transmission System-এ এ দুটি Circuit ব্যাপকভাবে ব্যবহৃত হয়।

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  5
  Digital Logic DesignKmap
  Solve the following function using K-map. F (w, x, y, z)= ∑(0,4,5,6,12,14,15)
  CB, SO(IT), 22 | Senior Officer (IT)
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  6
  Digital Logic DesignKmap
  Simplify the following boolean expression using 4 variable K-map F (A, B, C, D) = ∑ m(0,3,5,7,8,10,11,12,13,14,15). Draw the K-map grid, clearly show your groupings (loops), and write the final simplified Sum-of-Products (SOP) expression
  Combined Bank, SO(IT-24), 26 | Senior Officer (IT)
- ☆
  7
  Digital Logic DesignKmap
  Make a boolean expression using Karnaugh map: ∑m = (3,5,7,9,11,13,14,15)
  CB, AE(IT)/AHME/SO, 21 | AME/ANE/AE
- ☆
  8
  Digital Logic DesignKmap
  Simplify the following Boolean function using k-map and draw the logic circuit. F = A'B'C' + AB'C' + AB'C + A'BC + ABC
  JB, ANE, 20 | Assistant Network Engineer
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  9
  Digital Logic DesignBasic
  Determine whether the logical statement (P -> Q) -> (P' -> Q') is a tautology, contradiction, or contingency.
  ICB, AP, 26 | Assistant Programmer
  Determine whether the logical statement:
  (P → Q) → (P' → Q')
  Apply implication rules
  P → Q ≡ ¬P ∨ Q
  P' = ¬P
  Q' = ¬Q
  
  Therefore,
  P' → Q' = ¬P → ¬Q
  Construct the Truth Table
  P Q P → Q P' → Q' (P → Q) → (P' → Q')
  T T T T T
  T F F T T
  F T T F F
  F F T T T
  Conclusion
  Final column values: T, T, F, T
  
  Since the statement is true in some cases and false in one case, it is neither a tautology nor a contradiction.
  
  Therefore, the logical statement (P → Q) → (P' → Q') is a Contingency.
  In discrete mathematics, a contingency is a compound proposition whose truth value is neither always true (a tautology) nor always false (a contradiction). Its final outcome depends entirely on the specific truth values of its individual variables, meaning its truth table contains at least one True (T) and at least one False (F).
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  10
  Digital Logic DesignBasic
  Describe the important characteristics of digital IC's.
  CB, AME/AHE, 23 | AME/ANE/AE
  Important Characteristics of Digital Integrated Circuits (ICs)
  - Binary Representation: Digital ICs operate using binary values (0 and 1), which form the basis of digital data processing.
  - Boolean Logic: They are designed using Boolean algebra operations such as AND, OR, and NOT to perform logical functions.
  - Compactness and Integration: A large number of components can be integrated into a single chip, saving space and improving efficiency.
  - Low Power Consumption: Digital ICs consume less power than analog circuits, making them suitable for portable and battery-powered devices.
  - Noise Immunity: Binary signals provide better resistance to noise and interference, ensuring reliable operation.
  - High Speed: Digital ICs offer fast switching between logic states, enabling high-speed data processing.
  - Reliability: They provide stable, accurate, and consistent performance over long periods.
  Digital Integrated Circuits (ICs)-এর গুরুত্বপূর্ণ বৈশিষ্ট্যসমূহ
  - Binary Representation: Digital IC 0 এবং 1 (binary) ব্যবহার করে কাজ করে, যা digital data processing-এর ভিত্তি।
  - Boolean Logic: AND, OR এবং NOT-এর মতো Boolean operation ব্যবহার করে logic function সম্পাদন করে।
  - Compactness এবং Integration: একটি chip-এ বিপুল সংখ্যক component সংযুক্ত করা যায়, ফলে জায়গা সাশ্রয় হয় এবং দক্ষতা বৃদ্ধি পায়।
  - Low Power Consumption: Analog circuit-এর তুলনায় কম power ব্যবহার করে, তাই portable ও battery-powered device-এর জন্য উপযোগী।
  - Noise Immunity: Binary signal ব্যবহারের ফলে noise ও interference-এর প্রভাব কম হয় এবং নির্ভরযোগ্যভাবে কাজ করে।
  - High Speed: দ্রুত logic state পরিবর্তন করতে পারে, ফলে high-speed data processing সম্ভব হয়।
  - Reliability: দীর্ঘ সময় ধরে স্থিতিশীল, নির্ভুল ও নির্ভরযোগ্য performance প্রদান করে।
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  11
  Digital Logic DesignBasic
  Construct a Truth Table for a system that triggers an Alarm (Output 1) if: (Motion is Detected AND it is Night Time) OR (Panic Button is Pressed).
  Combined Bank, O(IT-22), 26 | Officer (IT)
  Truth Table for Alarm System Inputs: Motion Detected (M), Night Time (N), Panic Button Pressed (P) Output: Alarm (A)
  M N P Alarm (A)
  0 0 0 0
  0 0 1 1
  0 1 0 0
  0 1 1 1
  1 0 0 0
  1 0 1 1
  1 1 0 1
  1 1 1 1
  Boolean Expression: A = (M ∧ N) ∨ P
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  12
  Digital Logic Designkmap
  Simplify the following boolean expression using 4 variable K-map F(A, B,C,D)=m(0,3,5,7,8,10,11,12,13,14,15).
  Combined Bank, AE(IT)/AME, 26 | AME/ANE/AE
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  13
  Digital Logic DesignBasic Gate
  Draw the logic circuit for the Boolean expression Q = (A'B + BC(B + C)')'. Find the value of Q when (A, B, C) = (1, 0, 1).
  CB, AE(IT)/AME, 24 | AME/ANE/AE
  (A'B+BC(B+C)')'
  ∘ Substitute the values A = 1, B = 0, C = 1 into the equation.
  = (1'·0+0·1(0+1)')'
  = (0·0+0·1(0+1)')'
  = (0·0+0·1·1')'
  = (0·0+0·1·0)'
  = (0+0·1·0)'
  = (0+0)'
  = 0'
  = 1
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  14
  Digital Logic DesignBasic Gate
  Given a logical function, find out the truth table of AB· (A+B).C
  BB, AD(ICT), 25 | Bangladesh Bank
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  15
  Digital Logic DesignBasic Gates
  Draw the truth table from the follwoing circuit (2 bit input A,B full adder with carry bit Cin)
  Sonali Bank, ADA, 24 | ADA
  Inputs Outputs
  A B C_in S (Sum) C_out (Carry)
  0 0 0 0 0
  0 0 1 1 0
  0 1 0 1 0
  0 1 1 0 1
  1 0 0 1 0
  1 0 1 0 1
  1 1 0 0 1
  1 1 1 1 1
  S= A⊕B⊕Cin
  Cout= AB+Cin(A⊕B)
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  16
  Digital Logic DesignBasic Gates
  Simplify the Boolean algebra: Q = C' + A'B + BC'(B' + C) and draw a logic circuit.
  Sonali Bank, ADA, 24 | ADA
  
  Logic Circuit:
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  17
  Digital Logic DesignNumber System
  There are different number systems.
  (i) Convert (10010.101)₂=(?)₁₀ (ii) Convert (543)₁₀ =(?)₁₆
  CB, O(IT), 20 | Officer (IT)
  (i) Convert (10010.101)₂ to Decimal
  Binary Number = (10010.101)₂
  Integer Part:
  = (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰)
  = 16 + 0 + 0 + 2 + 0
  = 18
  Fractional Part:
  = (1 × 2^-1) + (0 × 2^-2) + (1 × 2^-3)
  = 0.5 + 0 + 0.125
  = 0.625
  Therefore,
  (10010.101)₂ = (18.625)₁₀
  (ii) Convert (543)₁₀ to Hexadecimal
  Successive Division by 16:
  Division Quotient Remainder
  543 ÷ 16 33 15 (F)
  33 ÷ 16 2 1
  2 ÷ 16 0 2
  Read the remainders from bottom to top:
  (543)₁₀ = (21F)₁₆
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  18
  Digital Logic Design
  For 7 segments display the input is abcdefg. When a decimal digit or value is display then its equivalent segment is high.
  (i) Find out the logical expression in Sum of product for 2bit binary input.
  Rupali, ANE, 21 |
  i) For 2 bit binary, we can find 00, 01, 10, 11 and the equivalent decimal value is 0,1,2,3.
  Now, For Binary= 00 (Decimal= 0)= abcdef is high
  For Binary= 01 (Decimal=1)= bc is high
  For Binary= 10 (Decimal=2) = abged is high For
  Binary=11 (Decimal=3)= abgcd is high
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  19
  Digital Logic Design
  Simplify the Boolean equation using K-map: F(A,B,C,D) = Σ(0,3,5,7,8,10,11,12,13,14,15).
  CB, AME/AE(IT-23), 26 | AME/ANE/AE
- ☆
  20
  Digital Logic Design
  Design a three-input XOR gate with the output function X=A⊕B⊕C using 2-input multiplexers.
  Dwasa,AME,25 | Other
  3-input XOR gate using 2:1 muxes: A 3-input XOR gate returns "1" when the odd number of inputs are "1". The truth table for 3-input XOR gate is shown in figure below.
  A B C O
  0 0 0 0
  0 0 1 1
  0 1 0 1
  0 1 1 0
  1 0 0 1
  1 0 1 0
  1 1 0 0
  1 1 1 1
  Truth table for 3-input XOR gate Let us choose A to be the select of mux closest to output. When A is "0", output is a function of B and C. So, we need another mux, let us choose B to be the select of this mux. Among the rows with A = 0, when B is "0", output is equal to C and when B is "1", output is equal to C'.
  Similarly among the rows with A = "1", when B is "0", output is equal to C' and when B is "1", output is equal to C. The implementation of 3-input XOR gate using 2:1 muxes is shown in figure below.
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  21
  Digital Logic Design
  Draw 16*8 RAM using 16*4 RAM.
  CB 3 Bank, SO(IT), 20 | Senior Officer (IT)
- ☆
  22
  Digital Logic Design
  Draw and write the output equation for 8 × 1 multiplexer:
  E S2 S1 S0 Output
  L L L L 0
  H H H H D7
  H H H L D6
  H H L H D5
  H H L L D4
  H L H H D3
  H L H L D2
  H L L H D1
  H L L L D0
  
  CB 3 Bank, SO(IT), 20 | Senior Officer (IT)
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  23
  Digital Logic Design
  7 segment display, a segment consists of BCD code that represent by ABCD, a segment is on by 2,3,5,6,7,8,9. Write the Boolean expression in SOP form and simplify with Kmap.
  CB 3 Bank, SO(IT), 20 | Senior Officer (IT)
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  24
  Digital Logic Design
  (12345)₁₀ = (?)₈
  So, (12345)₁₀ = (30071)₈
  BB, AP, 19 | Assistant Programmer
  To convert 1234510 to octal, repeatedly divide the number by 8 and record the remainders from bottom to top (MSB to LSB).
  Division Quotient Remainder
  12345 ÷ 8 1543 1
  1543 ÷ 8 192 7
  192 ÷ 8 24 0
  24 ÷ 8 3 0
  3 ÷ 8 0 3
  Read Remainders Upwards (Bottom to Top)↑
  (12345)10 = (30071)8
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  25
  Digital Logic DesignDecoder
  (ii) Draw logic circuit for 2to4 Line decoder/Demulltiplexer.
  Rupali, ANE, 21 |
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  26
  Digital Logic DesignAdder Circuit
  Draw a Full Adder circuit using two half adders.
  CB, SO(IT), 20 | Senior Officer (IT)

P	Q	P → Q	P' → Q'	(P → Q) → (P' → Q')
T	T	T	T	T
T	F	F	T	T
F	T	T	F	F
F	F	T	T	T

M	N	P	Alarm (A)
0	0	0	0
0	0	1	1
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	1

Inputs	Outputs
A	B	C_in	S (Sum)	C_out (Carry)
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	0	1
1	0	0	1	0
1	0	1	0	1
1	1	0	0	1
1	1	1	1	1

Division	Quotient	Remainder
543 ÷ 16	33	15 (F)
33 ÷ 16	2	1
2 ÷ 16	0	2

A	B	C	O
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	1
1	0	1	0
1	1	0	0
1	1	1	1

E	S2	S1	S0	Output
L	L	L	L	0
H	H	H	H	D7
H	H	H	L	D6
H	H	L	H	D5
H	H	L	L	D4
H	L	H	H	D3
H	L	H	L	D2
H	L	L	H	D1
H	L	L	L	D0

Division	Quotient	Remainder
12345 ÷ 8	1543	1
1543 ÷ 8	192	7
192 ÷ 8	24	0
24 ÷ 8	3	0
3 ÷ 8	0	3

Previous Job Question (Digital Logic Design)