Engineering College

2-derive the outputs' boolean equations (written in simplified forms) for decimal
to bcd priority encoder such that the smallest digit has the highest priority. show
all the steps for the simplification.

Answers

Answer 1

To derive the output Boolean equations for a decimal to BCD (Binary-Coded Decimal) priority encoder, we need to follow a step-by-step process. Let's assume the inputs are D3, D2, D1, and D0, representing the decimal input digits from 0 to 9.

Step 1: Determine the number of outputs required.

In a decimal to BCD priority encoder, we need four outputs to represent the BCD code for each decimal input digit. Let's denote the outputs as Y3, Y2, Y1, and Y0.

Step 2: Write the truth table.

Construct a truth table with inputs (D3, D2, D1, D0) and outputs (Y3, Y2, Y1, Y0) for all possible input combinations. In this case, the truth table will have 10 rows (corresponding to the decimal digits 0 to 9).

Step 3: Determine the outputs based on priority.

The priority encoder assigns a unique code to each input, giving priority to the smallest input digit. The priority order for the decimal digits is as follows: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Based on this priority, we can determine the outputs (Y3, Y2, Y1, Y0) for each decimal input digit in the truth table.

Step 4: Write the Boolean equations for each output.

To simplify the Boolean equations, we can use Karnaugh maps (K-maps) when the number of inputs is small. In this case, we have four inputs (D3, D2, D1, D0), which are convenient for K-map simplification.

Construct a separate K-map for each output (Y3, Y2, Y1, Y0) and fill in the corresponding output values based on the truth table.

Step 5: Simplify the Boolean equations using K-maps.

Analyze each K-map and group adjacent 1s to form product terms. These product terms will represent the simplified Boolean equations for the outputs.

Step 6: Write the final simplified Boolean equations.

Based on the simplified product terms obtained from the K-maps, write the final Boolean equations for each output (Y3, Y2, Y1, Y0).

Following these steps will allow you to derive the outputs' Boolean equations in simplified form for a decimal to BCD priority encoder with the smallest digit having the highest priority.

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Related Questions

a single-phase 50 kva, 2400–120 v, 60 hz transformer has a leakage impedance of (0.023 1 j 0.05) per-unit and a core loss of 600 watts at rated voltage

Answers

The leakage impedance of a single-phase 50 kVA, 2400-120 V, 60 Hz transformer is (0.023 + j0.05) per-unit.

The leakage impedance of a transformer represents the resistance and reactance of the winding that does not contribute to the power transfer. In this case, the leakage impedance is given as (0.023 + j0.05) per-unit. The real part, 0.023, represents the resistance, while the imaginary part, 0.05, represents the reactance. The per-unit value is used to normalize the impedance with respect to the rated values of the transformer.

The core loss of the transformer is given as 600 watts at rated voltage. Core loss refers to the power dissipated in the transformer core due to hysteresis and eddy current losses. It is important to consider the core loss when calculating the overall efficiency of the transformer.

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a new integration method based on the coupling of mutistage osculating cones waverider and busemann inlet for hypersonic airbreathing vehicles

Answers

Therefore, the phrase describes a new method of integrating multistage osculating cones, waverider, and Busemann inlet technologies to improve the performance of hypersonic airbreathing vehicles. This integration aims to enhance aerodynamic efficiency and reduce drag, ultimately leading to more efficient and faster vehicles.

The phrase "a new integration method based on the coupling of multistage osculating cones waverider and Busemann inlet for hypersonic airbreathing vehicles" refers to a method of combining different technologies to improve the performance of hypersonic airbreathing vehicles. Here is a step-by-step explanation:

1. Multistage osculating cones: These are structures that change shape at different stages of flight to optimize aerodynamic performance. They are used to reduce drag and increase efficiency.

2. Waverider: A waverider is a type of vehicle design that uses the shockwaves generated by its own supersonic flight to create lift. This design allows for increased aerodynamic efficiency at high speeds.

3. Busemann inlet: A Busemann inlet is a type of air intake design that reduces the effects of shockwaves during supersonic flight. It helps to slow down and compress the incoming air, increasing efficiency and reducing drag.

4. Integration method: The integration method mentioned in the question refers to combining the multistage osculating cones, waverider, and Busemann inlet technologies to create a more efficient and high-performing hypersonic airbreathing vehicle.

The phrase describes a new method of integrating multistage osculating cones, waverider, and Busemann inlet technologies to improve the performance of hypersonic airbreathing vehicles. This integration aims to enhance aerodynamic efficiency and reduce drag, ultimately leading to more efficient and faster vehicles.

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determine the mach number of a car moving in air (at 61of) at a speed of 177 mph (miles-per-hour). note: k for air may be assumed as 1.4; a useful gas constant might be 1716 ft-lb/slug-or.

Answers

The Mach number of the car moving in air at a speed of 177 mph is approximately 2.36.

To determine the Mach number of a car moving in air, we need to calculate the ratio of the car's velocity to the speed of sound.

- Speed of the car: 177 mph (miles per hour)

- Temperature of the air: 61 °F

First, let's convert the car's speed from mph to ft/s:

$$\text{Speed of the car} = 177 \, \text{mph} \times \frac{5280 \, \text{ft}}{1 \, \text{mile}} \times \frac{1 \, \text{hour}}{3600 \, \text{s}}$$

$$\text{Speed of the car} = 258.8 \, \text{ft/s}$$

Next, let's convert the air temperature from °F to °R (Rankine):

$$\text{Temperature of the air} = 61 \, \text{°F} + 459.67 \, \text{°R}$$

$$\text{Temperature of the air} = 520.67 \, \text{°R}$$

Now, let's calculate the speed of sound in the air using the equation:

$$\text{Speed of sound} = \sqrt{\gamma \cdot R \cdot T}$$

- $\gamma$ is the specific heat ratio for air (given as 1.4)

- $R$ is the specific gas constant for air (given as 1716 ft-lb/slug-°R)

- $T$ is the temperature of the air in °R

Substituting the values into the equation:

$$\text{Speed of sound} = \sqrt{1.4 \cdot 1716 \, \text{ft-lb/slug-°R} \cdot 520.67 \, \text{°R}}$$

$$\text{Speed of sound} = \sqrt{12087.288 \, \text{ft²/s²}}$$

$$\text{Speed of sound} = 109.76 \, \text{ft/s}$$

Finally, we can calculate the Mach number using the formula:

$$\text{Mach number} = \frac{\text{Speed of the car}}{\text{Speed of sound}}$$

$$\text{Mach number} = \frac{258.8 \, \text{ft/s}}{109.76 \, \text{ft/s}}$$

$$\text{Mach number} \approx 2.36$$

Thus, the appropriate answer is approximately 2.36.

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