EECS 1520 EXAM | 111 QUESTIONS AND ANSWERS |
2026 UPDATE | WITH COMPLETE SOLUTION
Moore's Law Answer - the observation that computing power roughly doubles
every two years (transistors)
Sampling Answer - converts continuous variation to discrete snapshots (eg
video 24-30 frames per second)
Trunctuation Answer - converting infinite large value ranges to a finite one (⅓ =
0.33333 stop at a certain point)
Digital vs analog signal - why 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 Answer - 2^8 = 256
Octal 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 Answer - Replace 4 bits, uses base 16
,What is two's complement? 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? 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 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? 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 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.
ASCII Answer - - Eight bits are used to represent one character (allowing 256
unique ones)
- First 32 are just characters that control how text appears
- 38 is decimal arabic numbers
- 65 is uppercase roman letters
- 97 is lower case roman letters
Unicode Answer - Uses 16 bits per character so can represent 2^16 characters
(65K +)
- First 256 of Unicode = same as ASCII
2026 UPDATE | WITH COMPLETE SOLUTION
Moore's Law Answer - the observation that computing power roughly doubles
every two years (transistors)
Sampling Answer - converts continuous variation to discrete snapshots (eg
video 24-30 frames per second)
Trunctuation Answer - converting infinite large value ranges to a finite one (⅓ =
0.33333 stop at a certain point)
Digital vs analog signal - why 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 Answer - 2^8 = 256
Octal 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 Answer - Replace 4 bits, uses base 16
,What is two's complement? 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? 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 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? 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 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.
ASCII Answer - - Eight bits are used to represent one character (allowing 256
unique ones)
- First 32 are just characters that control how text appears
- 38 is decimal arabic numbers
- 65 is uppercase roman letters
- 97 is lower case roman letters
Unicode Answer - Uses 16 bits per character so can represent 2^16 characters
(65K +)
- First 256 of Unicode = same as ASCII
