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Questions
Explain what a rational number is and give an example. (2 marks)
A rational number is any number that can be expressed directly as a fraction (1) e.g. any suitable fraction or whole number (1)
Explain the difference between a kibibyte and a kilobyte and state how many bytes each is. (2 marks)
A kibibyte uses powers of 2 and a kilobyte uses powers of 10. (1) A kibibyte is 1024 bytes and a kilobyte is 1000 bytes. (1)
Multiply the binary numbers 1100 and 11 (2 marks)
1100 x 11 = 1100 + 11000 (1) = 100100 (1)
Explain what two's compliment binary is and state the highest and lowest number that can be represented in whole number two's compliment binary using 6 bits. (3 marks)
A method for representing negative numbers where the most significant bit is negative. (1) Smallest -32 (1) Largest: 31 (1)
In two's compliment fixed point binary with 4 bits for the whole number part and 4 bits for the decimal part, what is represented by the decimal number 10010110 (1 mark)
-8 + 1 + .25 + .125 = -6.625 (1)
What is the value of the binary number 01100101 if it is a floating point number with 5 bits for the mantissa and bits for the exponent, both in two's compliment? (3 marks)
The mantissa 01100 is 0.375 (1) The exponent 101 is -3 (1) The result is 0.375 x 2-3 = 0.046875 (1)
Calculate the absolute and relative error of trying to store the number 0.1 as a 5 bit fixed point two's compliment number with 1 bit for the whole number part and 4 bits for the decimal part. (2 marks)
Closest representation is 0.125 so absolute error = .125 - .1 = .025(1) Relative error is 0.025/.1 x 100 = 25% (1)
Three numbers below are in two's compliment floating point binary with 6 bits for the mantissa and 4 bits for the exponent:
000101 0111
110111 1100
101111 0001
State which of these is normalised and explain how you know. (2 marks)
101111 0001(1) because a nromalised floating point number will always start either 01 or 10. (1)
Explain what even parity is and how it would affect the transmission of the 7 bits 1011001. (2 marks)
When transmitting 7 bit ASCII an eigth bit is added for error checking. Even parity is when it will add either a 1 or 0 in order to ensure there are an even number of 1s in the transmission. (1) So 1011001 would get a parity bit of 0 for even parity.
A transmission is received using majority voting as 111010000101. How will this be interpreted?(2 marks)
As 1001 because it is split into groups of 3 and the majority is taken as the transmitted bit. (2 marks)
Explain how a check digit is calculated (5 marks)
A check digit is calculated by assigning a weight of 1 to all the even digits i.e. the 1st, 3rd, 5th digits etc. and a weight of 3 to all the even digits i.e. the 2nd, 4th, etc. (1) Each digit is multiplied by it's weight (1) and the total of all weighted digits is calculated.(1) This number is divided by 10 using modulus and the remainder obtained.(1) This remainder is then taken away from 10. The result is the check digit. (1)
State two properties a vector rectangle might have. (2 marks)
Any 2 from:width, height, x position, y position, fill colour etc. 1 mark each property.
Explain whether a company logo should be a bitmap or vector image giving your reasoning. (3 marks)
A vector (1) because vectors are mathematically described (1) so can be scaled for billboards or business cards without pixelating. (1)
Explain how nyquist theorem applies to recording CDs. (3 marks)
Nyquist theorem says sounds need to be sampled at twice the highest rate in order to be reproduced accurately. (1) As people hear between 20 and approximately 20000Hz (1) the sample rate needs to be slightly more than double at 44100Hz. (1)
Explain how MIDI works. (3 marks)
Event messages (1) e.g. note, duration etc (1) are stored and can be played back as music. (1)
Explain how the Vernam cipher works. (3 marks)
A one time pad of truly random numbers as long as the data to be encrypted (1) is used as a key to encrypt a message using an XOR (1) and the key and the encrypted message are passed on to the recipient who can reverse the process with another XOR. (1)
The phrase "An eye for a tooth" is stored using the dictionary below. State how many bit will be used to store this compressed phrase and calculate the percentage saving over storing the same phrase in 8-bit ASCII (3 marks)
| Entry |
Text |
Binary |
| 1 |
An |
000 |
| 2 |
_eye |
001 |
| 3 |
_for |
010 |
| 4 |
_an |
011 |
| 5 |
, |
100 |
| 6 |
_a |
101 |
| 7 |
_tooth |
110 |
15 bits or just less than 2 bytes (1) (144-15)/144 x 100 (1) 89.58% (1)