Computer Science Exam 1

The von Neumann model states that both data and programs are stored in memory. This model, proposed by John von Neumann, is a fundamental concept in computer architecture. It describes a computer system with a central processing unit (CPU), memory, input/output devices, and a control unit. In this model, data and instructions for processing that data are stored in the same memory, allowing for the execution of programs and manipulation of data. Therefore, the correct answer is "data and programs are."

To convert a decimal number to binary, we can multiply the decimal part by 2 and keep track of the integer part at each step. In this case, we start with 0.625. We multiply by 2 and get 1.25. The integer part is 1, so we keep a 1. We then take the decimal part (0.25) and multiply by 2 again, getting 0.5. The integer part is 0, so we keep a 0. We repeat this process with the decimal part (0.5), multiplying by 2 to get 1.0. The integer part is 1, so we keep a 1. Finally, we take the decimal part (0.0) and multiply by 2, getting 0.0. Since the decimal part is now 0, we stop. Putting all the integers together, we get 0.101, which is the binary representation of 0.625.

The minimum sampling rate suggested for audio is 40,000 samples per second. This is because the Nyquist-Shannon sampling theorem states that in order to accurately reproduce a signal, the sampling rate must be at least twice the highest frequency present in the signal. The human hearing range typically extends up to 20,000 Hz, so a sampling rate of 40,000 samples per second ensures that all audible frequencies can be accurately captured.

Raster (or bitmap) graphics and vector graphics are two different methods of representing images. In raster graphics, the image is composed of a grid of pixels, where each pixel contains information about the color and intensity. On the other hand, vector graphics represent images using mathematical equations and geometrical shapes such as lines, curves, and polygons. These equations define the position, shape, and properties of the objects in the image. Therefore, the correct answer states that vector graphics encode images as geometrical equations, while raster graphics record the intensity of colors.

A True-Color scheme has 16,776,216 colors. This is because a True-Color scheme uses 8 bits each for red, green, and blue, resulting in 256 shades for each color. By combining these shades, we get a total of 256 x 256 x 256 = 16,776,216 possible colors.

The formula used to calculate the number of digits 'N' required in another base 'b' when converting from a decimal number is ceiling(log_b(N)). This formula takes the logarithm of 'N' with base 'b', then rounds up the result to the nearest integer using the ceiling function. The logarithm represents the power to which 'b' must be raised to obtain 'N'. The ceiling function ensures that any fractional part of the result is rounded up to the next whole number, as the number of digits cannot be a fraction.

To convert a binary number to decimal, we need to multiply each digit by the corresponding power of 2 and then sum them up. In this case, we have (110.11)2. The first digit from the right is 1, which represents 2^0. The second digit is 1, representing 2^1. The third digit is 0, representing 2^2. The fourth digit is 1, representing 2^-1. The fifth digit is 1, representing 2^-2. Multiplying each digit by the corresponding power of 2 and summing them up, we get (1*2^0) + (1*2^1) + (0*2^2) + (1*2^-1) + (1*2^-2) = 1 + 2 + 0 + 0.5 + 0.25 = 6.75.