Computer Systems Design · End Term · May 2026 · FN

In a 4-bit system, the one’s complement of the binary number 1000 is 1011.

A synchronous counter triggers all flipflops using a common clock signal, while an asynchronous counter triggers each flipflop using the output of the previous flipflop.

In a system with 65 unique states, 6 flipflops are sufficient to represent all the states.

In a decoder, at any point, exactly one of the outputs is 1 and all the rest are 0s.

According to Moore’s law, if a computer system has 2 million transistors today, then it will have approximately 32 million transistors in 4 years.

The given truth table has to be realized with D flipflop as shown below.

What is the equation for **Logic** in terms of A, B,

?

What is the minimum number of 2 input NOR gates required to design a circuit that implements the function

.

A 4-to-2 priority encoder has gates inputs

and

where

has the highest priority and

has the lowest priority. The output logic equations are given by

and

What is the output

when the input vector

? Note: Enter the answer as a two-bit binary value. For example, if the answer is (0, 0), enter it as 00.

A 1-bit comparator takes two input bits, A and B, and outputs **1** if A = B and **0** otherwise. Using only 2-input **NOR** gates, what is the minimum number of gates required to design such a comparator circuit?

We want to implement A ⊙ B (A XNOR B) using 2:1 multiplexers. What is the minimum number of 2:1 multiplexers required?

A circuit has four inputs: A, B, C, D and one output F. The output F is logic 1 if and only if exactly two of the four inputs are 0. In all other cases, the output is 0. What is the minimum number of minterms in the Sum of Products (SOP) expression for F?

Consider the circuit consisting of two D flipflops and one XNOR gate as shown below. The initial states are

= 0,

= 0, What is the number of possible states for the circuit?

Consider a mod-14 up counter with an initial state of 0011. What will be the state of the counter after 25 clock pulses?

Consider the circuit diagram using J-K flipflop as shown below. Assuming it was initially cleared to 0, state the output Y for the next 5 clock pulses.

Note: Do not write initial state as part of the answer. Your answer should be in the form:

Consider a 10-bit Johnson counter. What is the total number of unique states it can cycle through?

Consider a common bus architecture comprising of memory, and registers X, Y, Z. The control word format is given below.

What would be the control word if you intend to perform a register transfer from register X to register Z? Note: Enter the value in hexadecimal format (e.g. 0x24).

A processor contains 256 registers in its register file. The ALU of the processor supports 8 operations: addition, subtraction, multiplication, division, AND, OR, XOR, and NOR. What is the minimum number of bits required by an instruction to perform a subtraction operation between two operands stored in the register file, and store the result in a third register?

Consider the control word given below.

What is the maximum number of registers that can be stored in the instruction file?

Suppose we want to execute a data movement instruction, where we move the data present in register

to register

. **Instruction:**

Destination register,

Source register Operands: 0

d

31, 0

r

31 **Instruction Format:**

What will be the hexadecimal machine code for the instruction? Note: Enter the value in hexadecimal format (e.g., 0x2438).

Perform 2’s complement subtraction of two numbers A = 22 and B = 47. What is the result of A − B in 8-bit binary format? (Note: Don’t use sign-magnitude form.)