Computer Network Questions and Answers

Answer: A

Correct answer: 2 (m - 2)

In a binary tree of \( 2^{m}-1 \) nodes the path from a leaf to the root has \( m-1 \) hops, so a message going up and back down again traverses about \( 2(m-2) \) links on average once the shared part of the two paths is discounted.

Answer: A

Correct answer: successive values differ in exactly one bit

Gray code is an ordering of binary values in which each differs from the next in exactly one bit. For three bits it runs 000, 001, 011, 010, 110, 111, 101, 100. That single-bit property solves a real problem. When several bits change at once in ordinary binary - 0111 to 1000, for instance - they will not switch at precisely the same moment, and a reading taken during the transition can be wildly wrong. With Gray code only one bit ever changes, so the worst error is one count. It is therefore used in shaft encoders and position sensors, where a mechanical brush or optical reader may sample mid-transition. It is also why the axes of a Karnaugh map are labelled in Gray code: adjacent cells then differ in one variable, which is what makes grouping valid. Conversion from binary is simple: the first bit is copied, and each later bit is the XOR of the corresponding binary bit with the one before it.

Answer: C

Correct answer: move stored bits one position at each clock pulse

A shift register is a chain of flip-flops in which the output of each feeds the input of the next, so that on every clock pulse the whole pattern of bits moves one position along. The four configurations are named by how data enters and leaves. Serial-in serial-out is used for delay. Serial-in parallel-out converts a bit stream into a word, which is what a receiver does. Parallel-in serial-out does the reverse and is what a transmitter does. Parallel-in parallel-out acts as a simple storage register. Serial-to-parallel conversion is the reason shift registers are fundamental to communications, since data travels serially over a single line but is processed in parallel words. Shifting also performs arithmetic: shifting left multiplies a binary number by two and shifting right divides it by two, which is far cheaper in hardware than a multiplier. Feeding the output back to the input gives a ring or Johnson counter.

Answer: B

Correct answer: True

The statement is true. XNOR - exclusive NOR - gives 1 when its inputs are equal and 0 when they differ, which is the complement of XOR. Its truth table runs: 0,0 gives 1; 0,1 gives 0; 1,0 gives 0; 1,1 gives 1. For that reason it is also called the equivalence or coincidence gate, and its Boolean expression is \( AB + \bar{A}\bar{B} \). Its natural application is comparison. A chain of XNOR gates, one per bit pair, with their outputs ANDed together, forms an equality comparator: the result is 1 only if every bit matches. XOR does the opposite job and is used for parity generation and checking, since its output tells whether the number of 1s is odd. A useful identity: \( A \odot B = \overline{A \oplus B} \), so an XNOR is simply an XOR followed by an inverter, and the bubble on the symbol shows exactly that.

Answer: D

Correct answer: Shift register

A shift register is sequential, because it is built from flip-flops and its output depends on the bits already stored as well as on the present input. The other three are combinational: their outputs are determined entirely by their present inputs, with no memory of what came before. Each can be fully specified by a truth table. The dividing line is memory. Combinational circuits include adders, multiplexers, demultiplexers, decoders, encoders, comparators and code converters. Sequential circuits include flip-flops, latches, registers, shift registers and counters, and they need a clock. Sequential circuits are described by state tables and state diagrams, and they divide further into synchronous designs, where every element is clocked together, and asynchronous ones, where changes propagate as they occur. Every sequential circuit contains combinational logic inside it, generating the next state and the outputs, so the two categories are layered rather than opposed.

Answer: A

Correct answer: True

The statement is true. The 1’s complement simply changes each 0 to 1 and each 1 to 0, and in hardware it is a row of inverters. The 2’s complement goes one step further: invert every bit and then add 1. That extra step is what makes it the representation actually used for signed integers. The reason for preferring it is practical. 2’s complement has a single representation of zero, whereas 1’s complement has two - 00000000 and 11111111 - which complicates comparison. And 2’s complement addition needs no end-around carry: the same adder handles signed and unsigned values, so subtraction becomes addition of the complement and no separate subtractor is required. In eight bits, 2’s complement covers −128 to +127, the asymmetry arising from that single zero. 1’s complement is still met in checksum calculations, notably in the Internet protocols.

Answer: B

Correct answer: AND gate

The rules describe an output that is HIGH only when both inputs are HIGH and LOW in every other case, which is the AND function. An OR gate would be HIGH whenever either input was HIGH.

Answer: C

Correct answer: 10 base T

10Base-T runs twisted pair from each station to a central hub, which is a physical star. 10Base5 and 10Base2 are coaxial buses.

Answer: B

Correct answer: XOR gate

A half adder adds two bits and produces SUM = A ⊕ B from an XOR gate, while CARRY = A · B comes from an AND gate. XOR is the right choice because the sum bit is 1 exactly when the two inputs differ.

Answer: B

Correct answer: A + AB = A

The absorption law states A + AB = A, because whenever AB is true A is already true, so the second term adds nothing. It is one of the most useful simplifications when reducing an expression by hand.