ENG103 Digital Electronics Design SUSS Assignment Sample Singapore

ENG103 Digital Electronics Design course is an essential subject to understand the concepts of digital electronics design. The main objective of this course is to provide students with comprehensive knowledge in designing and constructing digital circuits. This course provides comprehensive coverage of logic gates, Boolean algebra, number systems, logic families, memory elements, and microcontrollers. It also covers topics such as combinational circuit design, arithmetic circuits, and digital communication systems.

This course aims to provide students with the essential skills and knowledge required in engineering practice. Students are expected to be competent in the use of digital design tools, including simulations and synthesis. They should also understand basic electrical principles and be able to apply them in their designs.

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This article will provide several outlines for assignments. These are as follows:

Assignment Outline 1: Give the conversion from one number system to another.

Here are some common number systems and their conversion methods:

Decimal to Binary: To convert a decimal number to binary, you can use the following steps:

Step 1: Divide the decimal number by 2.

Step 2: Write down the remainder (0 or 1).

Step 3: Divide the quotient of step 1 by 2.

Step 4: Write down the remainder.

Step 5: Repeat steps 3 and 4 until the quotient becomes 0.

Step 6: Write the remainders in reverse order to get the binary number.

Example: Convert 25 to binary.

Step 1: 25 ÷ 2 = 12 remainder 1

Step 2: 12 ÷ 2 = 6 remainder 0

Step 3: 6 ÷ 2 = 3 remainder 0

Step 4: 3 ÷ 2 = 1 remainder 1

Step 5: 1 ÷ 2 = 0 remainder 1

Step 6: The binary number is 11001.

Binary to Decimal: To convert a binary number to decimal, you can use the following steps:

Step 1: Write down the binary number.

Step 2: Assign each digit a power of 2, starting with 2^0 on the rightmost digit and increasing by 1 for each subsequent digit.

Step 3: Multiply each digit by its corresponding power of 2.

Step 4: Add up all the products to get the decimal number.

Example: Convert 11001 to decimal.

Step 1: The binary number is 11001.

Step 2: The rightmost digit has a power of 2^0, the second digit from the right has a power of 2^1, the third digit has a power of 2^2, and so on.

Step 3: Multiply each digit by its corresponding power of 2:

1 x 2^0 = 1

0 x 2^1 = 0

0 x 2^2 = 0

1 x 2^3 = 8

1 x 2^4 = 16

Step 4: Add up all the products: 1 + 0 + 0 + 8 + 16 = 25. Therefore, the decimal equivalent of 11001 is 25.

Decimal to Hexadecimal: To convert a decimal number to hexadecimal, you can use the following steps:

Step 1: Divide the decimal number by 16.

Step 2: Write down the remainder as a hexadecimal digit (0-9, A-F).

Step 3: Divide the quotient of step 1 by 16.

Step 4: Write down the remainder.

Step 5: Repeat steps 3 and 4 until the quotient becomes 0.

Step 6: Write the remainders in reverse order to get the hexadecimal number.

Example: Convert 255 to hexadecimal.

Step 1: 255 ÷ 16 = 15 remainder 15 (or F in hexadecimal)

Step 2: 15 ÷ 16 = 0 remainder 15

Step 3: The hexadecimal number is FF.

Hexadecimal to Decimal: To convert a hexadecimal number to decimal, you can use the following steps:

Step 1: Write down the hexadecimal number.

Step 2: Assign each digit a power of 16, starting with 16^0 on the rightmost digit and increasing by 1 for each subsequent digit.

Step 3: Convert each hexadecimal digit to its decimal equivalent (0-9, A-F).

Step 4: Multiply each digit by its corresponding power of 16.

Step 5: Add up all the products to get the decimal number.

Example: Convert 3A to decimal.

Step 1: The hexadecimal number is 3A.

Step 2: The rightmost digit has a power of 16^0, the second digit from the right has a power of 16^1, and so on.

Step 3: Convert each hexadecimal digit to its decimal equivalent: 3 = 3, A = 10.

Step 4: Multiply each digit by its corresponding power of 16:

3 x 16^0 = 3 x 1 = 3

10 x 16^1 = 10 x 16 = 160

Step 5: Add up all the products: 3 + 160 = 163. Therefore, the decimal equivalent of 3A is 163.

Binary to Octal: To convert a binary number to octal, you can group the binary digits into sets of three, starting from the rightmost digit, and then replace each set with its octal equivalent.

Example: Convert 1010111 to octal.

Step 1: Group the binary digits into sets of three: 1 010 111.

Step 2: Replace each set with its octal equivalent: 1 2 7.

Step 3: The octal number is 127.

Octal to Binary: To convert an octal number to binary, you can replace each octal digit with its binary equivalent.

Example: Convert 57 to binary.

Step 1: Replace each octal digit with its binary equivalent: 5 = 101, 7 = 111.

Step 2: The binary number is 101111.

Note: These are just a few examples of number system conversions. There are many other number systems, such as base 3, base 4, base 8, base 12, and so on, and each has its own conversion method.

Assignment Outline 2: Execute arithmetic operation on binary numbers.

Performing arithmetic operations on binary numbers is similar to performing them on decimal numbers, with the only difference being that there are only two digits, 0 and 1, instead of 0 through 9. Here are the steps to execute arithmetic operations on binary numbers:

Addition:

To add two binary numbers, follow these steps:

• Write the two numbers one below the other, aligning their bits vertically.
• Start adding from the right-most bit, just as you would do in decimal addition.
• If the sum of two bits is 0 or 1, write the sum under the line.
• If the sum of two bits is 2, write 0 under the line and carry over 1 to the next column to the left.
• Repeat this process until you have added all the bits.
• If there is a carry-over digit at the end, write it at the left end of the sum.1101 +1010 —– 10111

Subtraction:

To subtract one binary number from another, follow these steps:

• Write the two numbers one below the other, aligning their bits vertically.
• Start subtracting from the right-most bit, just as you would do in decimal subtraction.
• If the top bit is smaller than the bottom bit, borrow 1 from the next column to the left.
• Subtract the borrowed bit from the top bit and add 2 to the bottom bit.
• Repeat this process until you have subtracted all the bits.01 -1010 —– 11

Multiplication:

To multiply two binary numbers, follow these steps:

• Write the two numbers one below the other, aligning their bits vertically.
• Start multiplying from the right-most bit of the second number.
• If the right-most bit of the second number is 1, copy the first number below it and shift it one position to the left.
• If the right-most bit of the second number is 0, write a string of 0s below it.
• Add up all the numbers that you wrote down.

Division:

To divide one binary number by another, follow these steps:

• Write the dividend and the divisor one below the other, aligning their bits vertically.
• Start dividing from the left-most bit of the dividend.
• If the left-most bit of the dividend is smaller than the divisor, write a 0 below the dividend and shift one position to the left.
• If the left-most bit of the dividend is larger than the divisor, write a 1 below the dividend, subtract the divisor from the dividend and shift one position to the left.
• Repeat this process until you have divided all the bits.

Assignment Outline 3: Use Boolean algebra theorems and Karnaugh maps to simplify logic circuits.

Boolean algebra is a branch of algebra that deals with binary variables and logical operations. It is used in the design of digital circuits to simplify and optimize logic circuits. Boolean algebra theorems are used to manipulate and simplify logical expressions. Karnaugh maps, on the other hand, are graphical tools that provide a systematic method for simplifying Boolean expressions. In this response, we will demonstrate how to use both Boolean algebra theorems and Karnaugh maps to simplify logic circuits.

Boolean Algebra Theorems:

There are several theorems in Boolean algebra that are used to simplify logical expressions. Some of the most commonly used ones include:

1. Commutative Law: A + B = B + A and AB = BA
2. Associative Law: (A + B) + C = A + (B + C) and (AB)C = A(BC)
3. Distributive Law: A(B + C) = AB + AC and (A + B)(C + D) = AC + AD + BC + BD
4. Identity Law: A + 0 = A and A · 1 = A
5. Inverse Law: A + A’ = 1 and AA’ = 0
6. De Morgan’s Laws: (A + B)’ = A’B’ and (AB)’ = A’ + B’

Karnaugh Maps:

A Karnaugh map is a graphical tool used to simplify Boolean expressions. It is a table with cells that represent all possible combinations of the input variables. The cells are grouped together based on the input variables that are changing. The grouping of cells is based on the principle that adjacent cells in the table differ by only one variable. The Karnaugh map can be used to identify the minimal expression that represents the output of the logic circuit.

Assignment Outline 4: Recall the operation of flip-flops and basic logic circuits.

Flip-flops and basic logic circuits are fundamental building blocks of digital electronics, and are used to store and manipulate binary information.

A flip-flop is a circuit that has two stable states, either high or low, which it can be switched between by an input signal. The two most commonly used types of flip-flops are the D flip-flop and the JK flip-flop. In a D flip-flop, the input (D) controls the output (Q) and the output is the same as the input when the clock signal is high. In a JK flip-flop, the input (J) and (K) are used to set and reset the output (Q), respectively, and the output changes only when the clock signal is high.

Logic gates are used to perform logical operations on binary inputs. There are several types of logic gates, including AND gates, OR gates, NOT gates, XOR gates, and NAND gates. In an AND gate, the output is high only when both inputs are high. In an OR gate, the output is high when either input is high. In a NOT gate, the output is the opposite of the input. In an XOR gate, the output is high when one input is high but not both. In a NAND gate, the output is low only when both inputs are high.

By combining flip-flops and logic gates, more complex digital circuits can be built. For example, a counter circuit can be built using flip-flops to store the count value and logic gates to control the increment or decrement of the count. Other examples include adders, multiplexers, and decoders.

Assignment Outline 5: List the truth table for logic circuits.

A truth table is a valuable tool for analyzing logic circuits. It displays every possible input combination and corresponding output values. By using this table, we can easily determine a circuit’s behavior and make predictions about its functionality. Each row of the table represents one unique combination of inputs, and the outputs are listed in the adjacent columns.

As we work with larger and more complex circuits, truth tables become increasingly important for understanding how the circuit works. By presenting this information in a clear and organized manner, we can easily identify patterns and make logical connections between inputs and outputs. A truth table is a powerful tool that allows us to analyze circuit behavior and make informed design decisions.

Assignment Outline 6: Sketch the timing diagram.

When designing and analyzing digital circuits, a timing diagram is an essential tool for visualizing the order and duration of events. A timing diagram not only reveals the timing relationships between input and output signals but also helps to identify potential glitches or hazards that may occur during circuit operation. It consists of a horizontal axis that represents time and a vertical axis that represents the logical state of signals.

By using appropriate symbols, a designer can easily illustrate the transitions and delays of signals, making it easier to interpret circuit behavior. A well-designed timing diagram can save time and effort in troubleshooting, and improve the overall reliability of a digital system.

Assignment Outline 7: Design synchronous / asynchronous digital circuits.

Designing synchronous and asynchronous digital circuits involves different methodologies and techniques.

Synchronous circuits are those that rely on a clock signal to coordinate the flow of data between different elements. The clock signal acts as a timing reference and all elements in the circuit operate in sync with it. The design of synchronous circuits typically involves the following steps:

1. Define the functionality of the circuit and its inputs and outputs.
2. Choose a flip-flop type to use as the memory element in the circuit.
3. Use a hardware description language (HDL) such as Verilog or VHDL to describe the circuit’s behavior.
4. Use a synthesis tool to generate a netlist, which is a low-level representation of the circuit in terms of logic gates and flip-flops.
5. Use a place and route tool to map the netlist onto a physical FPGA or ASIC device.

Asynchronous circuits, on the other hand, do not rely on a clock signal and instead use signals called handshakes to coordinate the flow of data between different elements. The design of asynchronous circuits typically involves the following steps:

1. Define the functionality of the circuit and its inputs and outputs.
2. Choose a delay-insensitive protocol to use as the communication mechanism between different elements.
3. Use a HDL such as Petrify or Balsa to describe the circuit’s behavior.
4. Use a synthesis tool to generate a gate-level netlist, which is a low-level representation of the circuit in terms of logic gates.
5. Use a place and route tool to map the netlist onto a physical FPGA or ASIC device.

It is worth noting that asynchronous circuits are generally more complex to design and verify than synchronous circuits. However, they can offer advantages in terms of power consumption, speed, and robustness in noisy or uncertain environments.

Assignment Outline 8: Implement logic expressions using logic gates/ multiplexer/ encoder/ decoder.

Implementing logic expressions using logic gates, multiplexers, encoders, and decoders is an essential component of designing modern digital circuits. One fundamental reason to use these digital logic devices is to create complex logical functions that simplify the circuitry of more complex systems. When designing digital circuits, one must understand the principles of logic gates, multiplexers, encoders, and decoders to make necessary design decisions that maximize performance and minimize cost.

The usage of these devices allows engineers to create advanced technologies like digital displays, memory circuits, and communication devices more accurately and efficiently. Overall, designing digital circuits with these devices requires expertise and precision to ensure that the circuits function correctly and meet the needs of modern technology.

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