Fundamentals of data representation flashcards

Topic 5: Fundamentals of data representation

What is the difference between kibi and kilo prefixes?

Kibi (Ki) = 2¹⁰ = 1024; mebi (Mi) = 2²⁰; gibi (Gi) = 2³⁰. Kilo (k) = 10³ = 1000; mega = 10⁶; giga = 10⁹.

How do you represent a negative number in two’s complement?

Write the positive value in binary, invert all the bits and add 1. The most significant bit has a negative place value (−128 in 8 bits).

What is the difference between fixed point and floating point binary?

Fixed point: the binary point is in a set position, giving fixed precision and a limited range. Floating point: a mantissa and an exponent, giving a much greater range for the same bits.

Why is a floating-point number normalised?

To give the maximum precision for the number of bits: the mantissa starts 01 for a positive number or 10 for a negative one.

What is the difference between absolute and relative error?

Absolute error: the difference between the true value and the stored value. Relative error: the absolute error divided by the true value.

How do majority voting and check digits detect errors?

Majority voting: each bit is sent three times and the receiver takes the value that appears most often. Check digit: a digit calculated from the others and added to the end, recalculated to check the number.

What does Nyquist’s theorem state?

To reproduce a sound accurately, the sampling rate must be at least twice the highest frequency in the sound.

What is MIDI and what are its advantages?

Musical Instrument Digital Interface: music stored as event messages (note on/off, pitch, duration, instrument), not samples. Files are much smaller and easy to edit, but cannot store vocals.

What is the Vernam cipher, and why is it called perfectly secure?

Each character is XORed with a character of a random key (one-time pad) at least as long as the message, used only once. The ciphertext gives no information about the plaintext.

How do run-length encoding and dictionary-based compression work?

RLE: a run of repeated values is stored as one value and a count. Dictionary-based: repeated patterns are stored once in a dictionary and replaced in the data by their codes. Both are lossless.