GATE Computer Science Engineering(CSE) 2027 Test: Digital Logic - 1 Free

Given:

Distance = 2,896,819,200,000 metres

Concept used:

The standard form of a number is expressed in the powers of 10.

Solution:

Distance = 2,896,819,200,000 metres = 2.8968192 x 10¹² m

Hence, the correct option is A.

Concept:

The closure property of the multiplication of natural numbers states that the multiplication of two or more natural 
numbers always result in a natural number.  

Explanation:
Hence, two or more natural numbers multiplied results in a natural number.    
For example, 5 × 2= 10, is a natural number.

Hence, the Correct answer is False.

Input: When the signal enters the frequency counter it enters the input amplifier where the signal is converted into a rectangular logic wave for processing within the digital circuitry in the rest of the counter.

Accurate time-base / clock: In order to create the various gate/timing signals within the frequency counter an accurate timebase or clock is required.

Decade dividers and flip-flops: The clock oscillator is used to provide an accurately timed gate signal that will allow through pulses from the incoming signal. This is generated from the clock by dividing the clock signal by decade dividers and then feeding this into a flip-flop to give the enabling pulse for the main gate

Gate: The precisely timed gate enabling signal from the clock is applied to one input of a gate and the other has a train of pulses from the incoming signal. The resultant output from the gate is a series of pulses for a precise amount of time. For example, if the incoming signal was at 1 MHz and the gate was opened for 1 second, then 1 million pulses would be allowed through.

Counter/ latch: The counter takes the incoming pulses from the gate. It has a set of divide-by-10 stages (a number equal to the number of display digits minus 1). Each stage divides by ten and therefore as they are chained the first stage is the input divided by ten, the next is the input divided by 10 x 10, and so forth.

Display: The display takes the output from the latch and displays it in a normal readable format. LCD or LED displays are the most common. There is a digit for each decade the counter can display. Obviously, other relevant information may be displayed on display as well.

(A.A̅) + A

= 0 + A = A

All Boolean algebra laws are shown below:

D flip flop:

D flip flop has only one input terminal. The output of the D flip flop will be the same as the input. Hence, it is used in delay circuits.

The circuit is as shown below.

Logic symbol:

Truth table:

Characteristic equation: Q_n+1 = D

The D flip flop may be obtained from an S-R flip flop by just putting one inverter between the S and R as shown in the figure below.

S = R̅

The D flip flop may be obtained from a J-K flip flop by just putting one inverter between the J and K as shown in the figure below.

K = J̅

T flip flop:

T flip flop has only one input terminal. The output of the T flip flop will be toggled when the input is high on every new clock pulse. The output will be the same as the previous state when the input is low.

The circuit is as shown below.

Logic symbol:

Truth table:

Characteristic equation: Q_n+1 = TQ̅­_n + T̅Q_n

The T flip flop may be obtained from a J-K flip flop by making both the inputs are the same i.e. J = K.

• XR is not an example of logic gates.
• Logic gates are the electronic circuit performing logical operations having one or more than one input and only one output.
• They works on the principle of Boolean function.
• The various examples of logic gates are AND Gate, OR Gate, NAND Gate, NOR Gate, XOR Gate, etc.

Key Points

• Internally the computer coding scheme represents data in Binary form
• The computer is an electronic device, which accepts data, processes it and outputs the results in the form of reports.
• The original objective of computers was to make fast calculations, but modern computers besides performing fast calculations can store large volumes of data, process and retrieve data as and when desired.
• Hence computers are also known as data processors.
• The computer is a system. A system is a group of integrated parts to achieve a common objective.
• The computer is made up of integrated parts (input, control, ALU, storage, and output unit).
• All the parts work together to process data.
• The computer accepts input and outputs data in an alphanumeric form. Internally it converts the input data to meaning binary digits, performs the instructed operations on the binary data, and transforms the data from binary digit form to understandable alphanumeric form.

Concept:

1's complement of Binary: 1's complement of a Binary number is defined by the value obtained by inverting all the bit, i.e, 0 as 1 and 1 as 0.

∴ 1's complement of 1100 0110 = 0011 1001

2's complement of Binary: It is the sum of 1's complement of Binary number and 1 to the least significant bit (LSB).

∴ 2's complement = 1's complement + 1 (LSB)

Calculation:

Given Binary Number,

0011 0101 1001 1100

1's complement = 1100 1010 0110 0011

2's complement = 1's complement + 1 (LSB)

Concept used:

m⁰ = 1

Solution:

20 + 30 + 40 =1 + 1 + 1 = 3

20 × 30 × 40 = 1 x 1 x 1 = 1

(30 – 20) × 40 = (1 - 1) x 1 = 0 x 1 = 0

(30 – 20) × (30 + 20) = (1 - 1) x (1 + 1) = 0

Hence, the correct option is 2.

Concept:

• Flip-flop is a 1-bit memory cell which can be used for storing digital data.
• To increase the storage capacity in terms of the number of bits. A group of flip-flops is used. Such a group of flip-flops is known as a Register.
• A register capable of incrementing and/or decrementing its contents is called a counter
• A counter is a register capable of counting the number of clock pulses arriving at its clock input.
• A register is a group of flip-flops used to store multiple bits of data. An adder is a digital logic circuit in electronics that is extensively used for the addition of numbers.
• A latch is a circuit that has two stable states and can be used to store state information.
• The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs.