EECS 1520 Final Exam QUESTIONS AND
CORRECT ANSWERS
Moore's Law - CORRECT ANSWER the observation that computing power roughly doubles
every two years (transistors)
Sampling - CORRECT ANSWER converts continuous variation to discrete snapshots (eg
video 24-30 frames per second)
Trunctuation - CORRECT ANSWER converting infinite large value ranges to a finite one (⅓ =
0.33333 stop at a certain point)
Digital vs analog signal - why - CORRECT ANSWER - Cost, reliability, save energy
- Can be reclocked to regain original shape
- Noise produced by environmental effects causes fluctuation + degradation of the analog voltage
signal
How many numbers can you represent with 8 bits - CORRECT ANSWER 2^8 = 256
Octal - CORRECT ANSWER - Starting from least significant bit, replace groups of 3 bits with
a single octal digit
- Simply convert the octal digit to binary to get the binary replacement. So 1 = 001; 2 = 010; 3 = 011;
4 = 100, etc.
Hexadecimal - CORRECT ANSWER Replace 4 bits, uses base 16
What is two's complement? - CORRECT ANSWER - One of the possible ways to deal with
storing negative integers as binary
- Also has the benefit of getting rid of the double 0 that would appear normally in simple ordinary
signed representation (0000 and 1000 are both 0, wasting space)
- If the decimal number you want to convert to binary is positive, then convert and leave it at that.
- If the decimal number you want to convert to binary is negative, then:
, 1. Find the complement of the number by switching 1 and 0 (-5 --> 0101 --> 1010).
2. Add 1 to the complement (1010 + 1 = 1011).
3. To convert back, just change the bits back to decimal (0100), add one (0101), then convert,
remembering the sign (=-5).
Addition in two's complement? - CORRECT ANSWER - 2's complement is a fixed length
system. What this means is that
- When doing summations, i there is an overflow or carry, you must discard the carry bit.
Explain the problem of overflow in 2's complement - CORRECT ANSWER - The range of
values that you can store will be dependent on the number of bits you are working with. 2^(N-1)-1 to -
2^(N-1). Example for digits having 8 bits, you can represent +127 to -128.
- Now say you try to add 127+3. What you will actually end up with is -126. Why? Because it is not
possible store values above 127.
How can you represent decimal fractions in binary? - CORRECT ANSWER - Every number
past the decimal point will go 2^-1 (0.5), 2^-2 (0.25), etc.
- example: 2.75 = 10.11 (1*2 = 2; 1*0.5, 1*0.25)
- Multiplying the decimal portion by 2, which will give you another decimal digit starting with 1 or 0
before the decimal point. Take this value as the first binary digit. Take the decimal portion of that
value and multiply by 2 and repeat until it becomes 0 or you ran out of bits.
How to represent scientific notation - CORRECT ANSWER - + 53 2346 (DECIMAL)
- Take the number 234.56. In the "normalized form" we can write it as 0.23456*10^3
- Assume that in decimal the base is 10 and never changes and in normalized form the decimal point is
in a predictable location, so skip representing both of them
- Now what we have is the integer for the exponent (3) and a natural number (23456) for the mantissa
- The + indicates we are dealing with a positive integer.
- The 53 part gives two spaces representing the exponent. Since we have 2 spaces, we can represent
from 00 to 99. But remember exponents can also be negative, so we can only represent exponents
from -50 to +49.
- If you want to make the exponent positive, simply add 50.
CORRECT ANSWERS
Moore's Law - CORRECT ANSWER the observation that computing power roughly doubles
every two years (transistors)
Sampling - CORRECT ANSWER converts continuous variation to discrete snapshots (eg
video 24-30 frames per second)
Trunctuation - CORRECT ANSWER converting infinite large value ranges to a finite one (⅓ =
0.33333 stop at a certain point)
Digital vs analog signal - why - CORRECT ANSWER - Cost, reliability, save energy
- Can be reclocked to regain original shape
- Noise produced by environmental effects causes fluctuation + degradation of the analog voltage
signal
How many numbers can you represent with 8 bits - CORRECT ANSWER 2^8 = 256
Octal - CORRECT ANSWER - Starting from least significant bit, replace groups of 3 bits with
a single octal digit
- Simply convert the octal digit to binary to get the binary replacement. So 1 = 001; 2 = 010; 3 = 011;
4 = 100, etc.
Hexadecimal - CORRECT ANSWER Replace 4 bits, uses base 16
What is two's complement? - CORRECT ANSWER - One of the possible ways to deal with
storing negative integers as binary
- Also has the benefit of getting rid of the double 0 that would appear normally in simple ordinary
signed representation (0000 and 1000 are both 0, wasting space)
- If the decimal number you want to convert to binary is positive, then convert and leave it at that.
- If the decimal number you want to convert to binary is negative, then:
, 1. Find the complement of the number by switching 1 and 0 (-5 --> 0101 --> 1010).
2. Add 1 to the complement (1010 + 1 = 1011).
3. To convert back, just change the bits back to decimal (0100), add one (0101), then convert,
remembering the sign (=-5).
Addition in two's complement? - CORRECT ANSWER - 2's complement is a fixed length
system. What this means is that
- When doing summations, i there is an overflow or carry, you must discard the carry bit.
Explain the problem of overflow in 2's complement - CORRECT ANSWER - The range of
values that you can store will be dependent on the number of bits you are working with. 2^(N-1)-1 to -
2^(N-1). Example for digits having 8 bits, you can represent +127 to -128.
- Now say you try to add 127+3. What you will actually end up with is -126. Why? Because it is not
possible store values above 127.
How can you represent decimal fractions in binary? - CORRECT ANSWER - Every number
past the decimal point will go 2^-1 (0.5), 2^-2 (0.25), etc.
- example: 2.75 = 10.11 (1*2 = 2; 1*0.5, 1*0.25)
- Multiplying the decimal portion by 2, which will give you another decimal digit starting with 1 or 0
before the decimal point. Take this value as the first binary digit. Take the decimal portion of that
value and multiply by 2 and repeat until it becomes 0 or you ran out of bits.
How to represent scientific notation - CORRECT ANSWER - + 53 2346 (DECIMAL)
- Take the number 234.56. In the "normalized form" we can write it as 0.23456*10^3
- Assume that in decimal the base is 10 and never changes and in normalized form the decimal point is
in a predictable location, so skip representing both of them
- Now what we have is the integer for the exponent (3) and a natural number (23456) for the mantissa
- The + indicates we are dealing with a positive integer.
- The 53 part gives two spaces representing the exponent. Since we have 2 spaces, we can represent
from 00 to 99. But remember exponents can also be negative, so we can only represent exponents
from -50 to +49.
- If you want to make the exponent positive, simply add 50.
