EIT Computer Science and Numerical Methods 2

Question 1

In hexadecimal, what is the decimal value of FF?

Accepted Answer

255

Answer

FF in hex equals 15×16 + 15×1 = 240 + 15 = 255 in decimal.

Question 2

The central difference approximation for the first derivative f'(x) is:

Accepted Answer

[f(x+h) - f(x-h)] / (2h)

Answer

The central difference formula uses points on both sides of x and divides by 2h, providing second-order accuracy.

Question 3

The 4th-order Runge-Kutta method is primarily used to numerically solve:

Accepted Answer

Ordinary differential equations with initial conditions

Answer

RK4 is a step-by-step integration scheme that advances the solution of ODEs from initial conditions using weighted slope estimates.

Question 4

When the Newton-Raphson method converges near a simple root, its rate of convergence is:

Accepted Answer

Quadratic

Answer

Near a simple root, the error at each Newton-Raphson iteration is proportional to the square of the previous error — quadratic convergence.

Question 5

What is the result of the bitwise AND of binary 1100 and 1010?

Accepted Answer

1000

Answer

AND returns 1 only when both bits are 1: 1100 AND 1010 gives 1000 (only the leftmost bit is 1 in both).

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