Computer Science Number Systems and Logic Gates

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Questions and Answers

Convert (1101011)2 = ( )16

Convert (1111011)2 = ( )8

373

What are the triggering methods used for triggering flip flops?

Edge triggering, Level triggering

Define Minterm and Maxterm with respect to K-map.

Minterm is a product term in a boolean function, whereas Maxterm is a sum term. Signup and view all the answers

Define shift register and list its types.

A shift register is a sequence of flip-flops used to store multiple bits. Types include Serial In Serial Out (SISO), Serial In Parallel Out (SIPO), Parallel In Serial Out (PISO), and Parallel In Parallel Out (PIPO). Signup and view all the answers

List any two specifications of IC-DAC 0808.

Resolution: 8-bit, Operating voltage: 5V Signup and view all the answers

What is the logical circuit diagram of a half adder circuit?

A half adder consists of an XOR gate and an AND gate. Signup and view all the answers

Write the truth table of a D type flip-flop.

D | Q (Next State) 0 | 0 1 | 1 Signup and view all the answers

Convert (43)10 to BCD.

0100 0011 Signup and view all the answers

Convert (34)10 to Excess-3.

0111 0111 Signup and view all the answers

Convert (110111)2 to Gray code.

101101 Signup and view all the answers

Convert (11101)2 to 2's complement.

00011 Signup and view all the answers

Draw the logical diagram of a full adder using K-map simplification and write the truth table.

A full adder can be implemented using two XOR gates and two AND gates. Signup and view all the answers

Draw the block diagram of a programmable logic array (PLA) with proper labels.

A PLA typically includes an AND plane and an OR plane. Signup and view all the answers

Draw the circuit diagram of a BCD to 7-segment decoder and write the truth table.

The BCD to 7-segment decoder consists of specific logic gates that activate segments based on input BCD values. Signup and view all the answers

State and prove two De-Morgan’s Theorems.

Theorems: (¬A ∧ ¬B) = ¬(A ∨ B) and (¬A ∨ ¬B) = ¬(A ∧ B). Proved using truth tables. Signup and view all the answers

Draw basic gates AND, OR and NOT using NAND gates only.

AND: NAND followed by NOT; OR: NAND gates with inputs fed to same gate; NOT: Single NAND with both inputs tied. Signup and view all the answers

Draw a 4-bit ring counter with truth table and its waveform.

A 4-bit ring counter cycles through states with a single high bit shifting left. Signup and view all the answers

Compare Volatile and Non-volatile memory.

Volatile memory requires power to maintain data; non-volatile retains data without power. Signup and view all the answers

Compare SRAM and DRAM memory with two points each.

SRAM: Faster access time, more expensive. DRAM: Slower access time, cheaper. Signup and view all the answers

Realize the boolean expression y = AB + BC (B + C) using basic gates and simplify.

The expression can be realized using AND and OR gates, then simplified to fit the requirements. Signup and view all the answers

Design a 4-bit binary to Gray code converter using truth table.

The truth table shows the relationship between binary input and Gray output, with specific bits calculated. Signup and view all the answers

Realize given expression using K-map: f(A, B, C, D) = Σ m (3, 5, 7, 8, 10, 11, 12, 13).

The minimal expression can be derived from grouping the ones in the K-map. Signup and view all the answers

Draw the JK master-slave flip flop and explain its operations.

The JK master-slave flip flop changes output on the clock edge, allowing feedback. Signup and view all the answers

Calculate the analog output of a 4-bit DAC for digital input 1100. Assume VFS = 5V.

The analog output is 3.75V. Signup and view all the answers

Draw and explain the operation of a 4-bit universal shift register. Draw necessary waveforms.

A universal shift register can shift left, shift right, and hold data, controlled by specific control signals. Signup and view all the answers

Draw the block diagram of a Dual slope ADC and explain its working.

A Dual slope ADC compares input voltage to a ramp signal and integrates over a period. Signup and view all the answers

Subtract following using Two’s complement method: (15)10 - (32)10.

Convert both numbers to binary, find two's complement for 32, then add. Signup and view all the answers

Design a MOD-12 ripple counter. Write its truth table with waveform.

The MOD-12 counter counts from 0 to 11 and then resets, with specific states defined in the truth table. Signup and view all the answers

Design a 16:1 multiplexer using 4:1 multiplexer.

Connect four 4:1 MUXs to create the required 16:1 MUX. Signup and view all the answers

Compare TTL and CMOS for the following points: Fan In, Fan Out, Propagation delay, Power dissipation.

TTL has lower fan out and higher power dissipation compared to CMOS, which has better fan in and lower delays. Signup and view all the answers

Study Notes

Number Systems

Conversion between binary, hexadecimal, and octal number systems is a core concept.
Example: (1101011)2 = (6B)16 and (1111011)2 = (173)8
BCD (Binary Coded Decimal): Represents decimal digits using 4-bit binary.
Excess-3: Adds 3 to each BCD digit, providing self-complementing property.
Gray code: Each code differs from the previous by one bit, eliminating ambiguity in transitions.
Two's Complement: Used for representing negative numbers in binary.

Logic Gates and Boolean Algebra

Basic Gates: AND, OR, NOT
NAND Gate is universal, meaning it can be used to build all other gates
De Morgan's Theorems: Provide rules for simplifying Boolean expressions using NOT, AND, and OR gates:
- NOT(A AND B) = (NOT A) OR (NOT B)
- NOT(A OR B) = (NOT A) AND (NOT B)

Combinational Circuits

Half Adder: Adds two single bits, producing a sum and carry.
Full Adder: Adds three bits, using two half adders.
K-Map (Karnaugh Map): A graphical method for simplifying Boolean expressions.
BCD to 7-Segment Decoder: Converts BCD code to activate segments in a 7-segment display.
Programmable Logic Array (PLA): A programmable logic device that can implement a wide range of logic functions.

Sequential Circuits

Flip-Flops: Digital circuits that can store a bit of information. Common types are:
- D type flip-flop: Stores the value of input D when a clock pulse arrives.
- JK flip-flop: Stores the value of input J or K, depending on the current state.
- Master-Slave Flip-Flop: Combines two flip-flops to prevent race conditions during clock transitions.
Shift Registers: Circuits that shift data bits with each clock pulse. Types include:
- Serial-in, Serial-out: Input and output data sequentially.
- Serial-in, Parallel-out: Input data sequentially, output data in parallel.
- Parallel-in Parallel-out: Load and output data in parallel.
Ring Counter: A type of shift register that cycles through a sequence of states, useful for implementing counters.
Counters: Circuits that count events using flip-flops and logic gates.

Memory

SRAM (Static RAM): Uses latches to store data, fast but power-consuming.
DRAM (Dynamic RAM): Uses capacitors to store data, slower but less power-consuming.
Volatile Memory: Loses its contents when power is removed.
Non-volatile Memory: Retains its contents even when power is removed.

Analog-to-Digital Converters (ADC)

Dual Slope ADC: A type of ADC that uses a ramp generator and integrator to convert an analog voltage to digital.

Digital-to-Analog Converters (DAC)

DAC 0808: A common type of IC DAC that can convert binary inputs to analog output voltages.

Other Important Concepts

Mux (Multiplexer): Selects one of multiple input signals based on a control signal.
TTL (Transistor-Transistor Logic): A logic family using bipolar transistors.
CMOS (Complementary Metal-Oxide Semiconductor): A logic family using MOSFET transistors, known for low power consumption.
Fan-In: The number of inputs a logic gate can handle without affecting its operation.
Fan-Out: The number of outputs a logic gate can drive without affecting its operation.
Propagation Delay: The time it takes for a signal to pass through a logic gate.

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Description

This quiz covers essential concepts in number systems, including binary, hexadecimal, and octal conversions, as well as BCD and Gray code. Additionally, it delves into the basics of logic gates, Boolean algebra, and combinational circuits like adders. Test your understanding of these fundamental computer science topics.