Digital Electronics Test 2

(146)_b + (313)_b-2 = (246)₈

b² + 4b + 6 + 3(b-2)² + (b-2) + 3 = 2× 8² + 4×8 + 6

4b² – 7b + 19 = 166

 4b² – 7b – 147 = 0

4b² – 28b + 21b – 147 = 0

4b(b –  7) + 21(b – 7) = 0

(b – 7).(4b + 21) = 0

∴ b = 7 or b = -21 ÷ 4

Since b cannot be negative or in fraction

∴ b = 7

Alternate Method:

Substitute and check the result

b = 7

(146)₇ + (313)_7-2 = (246)₈

LHS = (146)₇ + (317)_7-2

 (146)₇ = 1 × 7² + 4 ×7¹ + 6 × 7⁰ = 49 + 28 + 6 = (83)₁₀

(313)₅ = 3 × 5² + 1 × 5 + 7× 5⁰ = 75 + 5 + 3 = (83)₁₀

LHS = (83)₁₀ + (83)₁₀ = (166)₁₀  

RHS = (246)₈

= 2 × 8² + 4 ×8¹ + 6 × 8⁰

= 128 + 32 + 6 = (166)₁₀  

The enable input is also known as strobe which is used to cascade two or more multiplexer ICs to construct a multiplexer with a larger number of inputs. Enable input activates the multiplexer to operate.

The overall modulus of the cascaded counter is the multiplication of the modulus of the individual counters.

Overall modulus (N) = 4 × 5 × 6 = 120

The clock frequency (f_clk) = 12 MHz

The lowest output frequency \(= \frac{{{f_{clk}}}}{N}\) 

\(= \frac{{12 \times {{10}^6}}}{{120}} = 100\;kHz\)

Data Selector is another name of Multiplexer. A multiplexer (or MUX) is a device that selects one of several analog or digital input signals and forwards the selected input into a single line, depending on the active select lines.

The major functioning responsibility of the multiplexing combinational circuit is generation of selected path between multiple sources and a single destination because it makes the circuit too flexible. A multiplexer (or MUX) is a device that selects one of several analog or digital input signals and forwards the selected input into a single line, depending on the active select lines.

The elevator door will open in the following two cases:

Case I: If the elevator is stopped and is level with the floor and the time has not expired

So we’ll have the representation as:

Elevator is stopped = E

Level with the floor = F

Time has not expired = T̅

So, the given condition is expressed as –

X₁ = SFT̅

Case 2: If the elevator is stopped and is level with the floor and a button is pressed.

Again we have the representation as:

Elevator is stopped = S

Level with the floor = F

Button is pressed = B

So, the given condition is expressed as;

X₂ = SFB

Since the door will open in Case-1 ‘OR’ Case-2.

Therefore, we may express the condition for the elevator door to open as D = X₁ or X₂, i.e.

Concept: 

A decoder with k input lines has 2^k output lines.

Calculation:

The memory is byte-addressable. So 64 KB = 2¹⁶ B.

16 × 2¹⁶ decoders.

So, the number of input lines (p) = 16

Number of output lines (q) = 2^p = 2¹⁶ = 65536

∴ p + q = 16 + 65536 = 65552 

The resolution of a 4-bit counting ADC = 0.5 V

That means the voltage corresponding to each count = 0.5 V

For an input of 5.1 V, the number counts that counter will count

\(= \frac{{5.1}}{{0.5}} = 10.2 \approx 1\) 

Digital output = 1011

Maximum conversion time = (2ⁿ - 1) T_clk

Clock frequency (f) = 0.5 MHz

\({T_{clk}} = \frac{1}{f} = \frac{1}{{0.5\; \times \;{{10}^6}}} = 2\;\mu s\) 

Maximum conversion time = (2⁴ - 1) × 2 μs = 30 μs  

A multiplexer (or MUX) is a device that selects one of several analog or digital input signals and forwards the selected input into a single line, depending on the active select lines. Since many operational behaviour can be performed by using a multiplexer. Whereas, a combinational circuit is a combination of many logic gates which makes the circuit more complex.

The word demultiplex means “one into many” and distributor. A demultiplexer sends a single input to multiple outputs, depending on the select lines. It is clear from the diagram:

A demultiplexer sends a single input to multiple outputs, depending on the select lines. Demultiplexer converts single input into multiple outputs.

A demultiplexer sends a single input to multiple outputs, depending on the select lines. As the select input changes, the output of the multiplexer varies according to that input.

The number of AND gates required will be equal to the number of outputs in a demultiplexer, which are 8.

IC 74154 is used for the implementation of 1-to-16 DEMUX, whose output is inverted input.

A demultiplexer sends a single input to multiple outputs, depending on the select lines. For one input, the demultiplexer gives several outputs. That is why it is called a data distributor.

The formula for total no. of outputs is given by 2n, where n is the no. of select lines. Therefore, for 1:4 demultiplexer, 2 select lines are required.

The 4-bit output is b₃ b₂ b₁ b₀

Resolution \( = \frac{{15}}{{{2^4} - 1}} = 1\;V\)

For input V_i = 2V:

Output code word: 0001

For input V_i = 1 V:

Output code word: 0001

For input V_i = 4 V:

Output code word: 0100

For input V_i = 6 V:

The number of AND gates required will be equal to the number of outputs in a demultiplexer, which are 8.

The output Y₄ = S₂.(S₁)’.(S₀)’.I. since the bit combinations of 4 are 100.

The large reverse current flow in zener diode is due to rupturing-off or tearing-off of covalent bends within the depletion layer. This phenomena is called zener breakdown phenomena, It is due to large electric field intensity.

The work function of a metal represents the minimum amount of energy that must be given to the fastest-moving electron at the absolute zero of temperature in order for this electron to be able to escape from the metal. Hence, low work function (E_w) is required for thermionic emission.

Hence, when forward bias is applied to a p-n junction diode, width of the depletion layer is reduced i.e. potential barrier is decreased

In a p-n junction tunnel diode, the depletion layer width is negligible and therefore, the charge carriers will be penetrating the depletion layer almost at the speed of light and this property is called tunnelling of charge carriers across the junction.

The energy level diagram for a semiconductor is shown below.

E_G is called “band gap” or "forbidden energy gap” which lies between the valence band and the conduction band.

In an intrinsic semiconductor, as the temperature increases mobility is slightly reduced since mobility of charge carrier is inversely proportional to temperature. This will slightly reduce the conductivity. But, due to temperature effect, large number of covalent bonds are broken which creates electrons and holes and this increases the conductivity by a larger value. As a result of this resistivity is decreased