GATE Computer Science Engineering(CSE) 2027 Test: Digital Logic - 2 Free

Hexadecimal is a number system with a base 16. We can divide the word HEXA+DECIMAL for better understanding; it means 6 and 10 make 16.
It is the easiest way to write and count numbers represented in terms of base 16.
There are sixteen distinct digits in the hexadecimal system, it starts from 0, 1,2,3,4,5,6,7,8,9, A, B, C, D, E and end to F.
Where A= 10, B=11, C=12, D=13, E=14, F=15.
It is usually represented by 4 bits in binary number system by 8421 code.

If you want to convert a hexadecimal number into an octal number, the first thing you need to do is convert a hexadecimal number into binary form by writing the binary equivalent of each digit in the form of 4 bits. Once you write the number into binary form, you need to group the binary equivalent in 3 bits, then for each of the three bits, the respective digit is written.

(1E.43)₁₆ = (0001 1110.0100 0011)₂

= (00011110.01000011)₂

= (011110.010000110)₂

= (011 110.010 000 110)₂

= (36.206)₈

BCD stands for Binary Coded Decimal. It is a type of binary encoding where each decimal digit is represented by a fixed number of bits, usually 4. It is also called 8421 code to represent the maximum number 15. BCD can encode only from 0-9. For example, Decimal number 456, its equivalent BCD code is 0100 0101 0110

SCR stands for Silicon Controlled Rectifier; it is a family of thyristors with the same property as thyristors. It is a semiconductor device with three junctions. They are of two types: npnp and pnpn. For the pnpn type, the inner player has a gate terminal, the outer player has an anode terminal, and the outer n layer has a cathode terminal. The SCR controls the flow of anode current once the gate is triggered.

NAND or NOR gates are used to design all other logic gates, so; they are termed universal gates.

Toggling means switching between the two states when output changes to its complement on applying clock signal. For example, suppose you assume the initial output to be X (1 or 0), then after toggling, the output state will be X' (0 or 1, respectively). Both j and k should be 1 for toggle in JK flip flop.

The terminologies like MSI, SSI, LSI and VLSI came out from the complexity of the integrated circuit. It means the total number of transistors are fabricated on a single chip. Jack Kilby invented the first integrated circuit in 1959, so, after that, the Integrated circuit has emerged like SSI, LSI, MSI and VLSI.

In MSI (Medium Scale Integration) = 30 - 300 gates /chip (counters, multiplexers, registers)

In LSI (Large Scale Integration) = 300 - 3000 gates /chip (8-bit processors)

In SSI (Small-Scale Integration) = 3 - 30 gates /chip (logic gates, flip flops)

In VLSI (Very Large-Scale Integration) = >3000 gates / chip (16 bit and 32- bit processors)

As we know, the total number of states in the Jhonson counter is determined by the given formula

2^N = 2 ⁸= 256

Now,

the total number of used states = 2N = 2* 8 = 16

therefore, the total number of unused states = 256-16 = 240

The operating frequency refers to the frequency at which the communications are being made with the total bandwidth occupied by the carrier signal with modulation.

The transistor's current gain, denoted as β (beta), is calculated using the formula:

• β = Ic / Ib
• Ib = Ie - Ic

Given:

• Ie = 100.2 mA
• Ic = 100 mA

Calculate Ib:

• Ib = 100.2 mA - 100 mA = 0.2 mA

Calculate β:

• β = 100 mA / 0.2 mA = 500

The correct answer is C: 500.