Computer Network Questions and Answers

Answer: C

Correct answer: both inputs are HIGH

A NAND gate is an AND gate followed by an inverter, so its output is the complement of AND. AND gives 1 only when both inputs are 1; NAND therefore gives 0 only in that single case and 1 in the other three. Its truth table is worth holding in mind: 0,0 gives 1; 0,1 gives 1; 1,0 gives 1; 1,1 gives 0. NAND is called a universal gate because every other logic function can be built from it alone. An inverter is a NAND with both inputs tied together; an AND is a NAND followed by another NAND acting as an inverter; an OR is a NAND fed by two inverting NANDs, which is De Morgan’s theorem in hardware. NOR is universal for the same reason. That property matters in practice, since a manufacturer can build an entire logic family from one repeated cell.

Answer: C

Correct answer: \( A + A = A \)

The idempotent law states that combining a variable with itself changes nothing: \[ A + A = A, \qquad A \cdot A = A. \] This is one of the clearest departures from ordinary arithmetic, where \( A + A = 2A \) and \( A \cdot A = A^{2} \). In a two-valued algebra there is no 2 and no square, so the operation simply returns the value unchanged. The other options are the remaining basic identities, each with its own name. \( A + \bar{A} = 1 \) is the complement law, with dual \( A \cdot \bar{A} = 0 \). \( A + 0 = A \) is the identity law, with dual \( A \cdot 1 = A \). And \( A + 1 = 1 \) is the null or annulment law, with dual \( A \cdot 0 = 0 \). Each pair is a dual of the other, obtained by exchanging AND with OR and 0 with 1 - a symmetry that runs through the whole of Boolean algebra and halves the amount to be memorised.

Answer: C

Correct answer: 4

A counter built from \(n\) flip-flops passes through \(2^n\) states, so a MOD-16 counter needs \(n = 4\) since \(2^4 = 16\). It counts 0 through 15 and then returns to 0.

Answer: B

Correct answer: 15

Octal is base 8, so each digit carries a place value that is a power of eight. For 17 that gives \[ 1 \times 8 + 7 = 15. \] The trap is reading the numeral as though it were decimal, which is why 17 is offered as a distractor. Octal uses only the digits 0 to 7; the digits 8 and 9 do not exist in it, so a numeral containing either is not a valid octal number at all - a quick way to spot a bad option. Octal is used as shorthand for binary because each octal digit corresponds to exactly three bits: 1 is 001 and 7 is 111, so 17 in octal is 001111, which is 15. Conversion is done by grouping bits in threes from the right, with no arithmetic. It was common on machines with word lengths divisible by three, and survives in Unix file permissions, where 755 and 644 are octal.

Answer: B

Correct answer: Successive values differ in exactly one bit

In Gray code only one bit changes between consecutive values. That property matters in position encoders, where several bits changing at once could momentarily be read as a wildly wrong value.

Answer: C

Correct answer: Registers and cache

Registers sit inside the processor itself, and cache - at least its first level - is fabricated on the same die, so both are reached without a transaction on the external memory bus. That proximity is what makes them fast. The memory hierarchy arranges storage by the trade-off between speed, capacity and cost per bit. Registers are fastest and smallest; L1, L2 and L3 cache follow; then main memory in DRAM; then solid-state and magnetic disk; then optical media and tape at the bottom, slowest and cheapest. Everything below cache is reached over a bus and takes hundreds or millions of cycles rather than one. Only the top three levels are directly addressable by instructions at all. Disk, optical media and tape are secondary storage: their contents must be copied into main memory before the processor can operate on them, which is what an operating system’s input and output subsystem exists to arrange.

Answer: D

Correct answer: Three

A full adder takes three inputs - the two bits being added and a carry-in from the previous stage - and produces a sum and a carry-out. That carry-in is exactly what a half adder lacks, which is why half adders cannot be chained.

Answer: C

Correct answer: simplify Boolean expressions

A Karnaugh map is a graphical method of minimising a Boolean expression. It arranges the cells of a truth table so that any two adjacent cells differ in exactly one variable, which lets a redundant variable be spotted and cancelled by grouping. That adjacency is achieved by labelling the axes in Gray code - 00, 01, 11, 10 rather than 00, 01, 10, 11 - and the map wraps at its edges, so the leftmost and rightmost columns are also adjacent. Groups must contain a power of two cells: 1, 2, 4, 8. Each doubling of a group removes one variable from the resulting term, so the aim is to cover every 1 with as few and as large groups as possible. Overlapping is allowed. Cells marked as don’t care may be treated as 1 or 0, whichever makes the groups larger. The map is practical up to four variables; beyond that the Quine–McCluskey algorithm is used instead.

Answer: C

Correct answer: one variable

Adjacent cells in a Karnaugh map differ in exactly one variable, and that single property is what makes the map work. When two adjacent cells both contain 1, the variable that differs between them can be eliminated. Algebraically this is the identity \[ A B + A \bar{B} = A(B + \bar{B}) = A. \] Combining a pair removes one variable, a group of four removes two, a group of eight removes three. The arrangement is achieved by labelling the axes in Gray code, in which successive values change one bit at a time: 00, 01, 11, 10. Plain binary order would place 01 next to 10, which differ in two bits, and the grouping would be invalid. The map also wraps round, so the first and last columns are adjacent, and in a four-variable map the four corner cells form a valid group of four. Missing that wraparound is the commonest error in using the method.

Answer: C

Correct answer: 3

A multiplexer with \( n \) select lines can choose among \( 2^{n} \) inputs, so for eight inputs \[ 2^{n} = 8 \quad\Rightarrow\quad n = 3. \] The three select lines form a binary address: 000 routes input 0 to the output, 001 routes input 1, and so on up to 111 for input 7. The same relation gives 2 select lines for a 4-to-1 multiplexer and 4 for a 16-to-1. It is the identical arithmetic that determines the number of flip-flops in a counter and the number of address lines for a memory, so it is worth being fluent in both directions. Multiplexers are used for far more than data routing. Because a \( 2^{n} \)-to-1 multiplexer can implement any Boolean function of \( n \) variables directly - by wiring the truth table values to its data inputs - it serves as a general-purpose logic element, which is why lookup tables in field-programmable gate arrays are built this way.