CS-1100 Discrete Math
Convert 11011.001 to decimal
27 & 1/8
Do the following addition problems in the base indicated: AD3E (hex) +2FE9 -----
DD27
Convert -500 to decimal using two's complement notation. Use 9 bits please.
I cannot represent this number correctly given the number of bits
Is the following true or false? 3 > 2 and 8 < 7
Is the following true or false? 3 > 2 and 8 < 7
Can I convert the hex number 8383 to binary?
True
11110110
can't - not enough bits
Do the following subtraction problems in the base indicated: 100001 (binary or base 2) -11111 -------
10
For the following binary number, match the correct answers: 111010110101 Hexadecimal Octal
EB5 7265
A = (Boston, Buffalo, Cleveland, Los Angeles, Dallas, Boone, Seattle, Anchorage} |A| = 9
False
A = {2,4,6,8.10} Is x \in A if x=12?
False
A = {2,4,6,8.10} Is x \in A if x=8?
False
A = {5,10,15,20,25} B = {x: x mod 5 = 0 ; x<30} A U B = {5,10,15,20,25,30}
False
D = {x: 5 < x < 31, x is an integer} E = {5,10,15,20,25,30} Is D = E?
False
I can convert the octal number 8383 to binary.
False
It is possible to express +128 in 8 bits using two's complement notation? If so, then write it below.
False
Let A = { a, {} }. a is a subset of A
False
Let A = { a, {} }. {a} is an element of A
False
Match the following metric prefixes with their computer-based values 10^30 10^10 10^20 10^40
Giga Kilo Mega Tera
What is the correct negation of the following statement? I do not fish or waterski
I do not fish and I do not waterski
Which of the following is the contrapositive for the following statement? If bells ring then the angels sing.
If angels do not sing then bells do not ring.
Let w, b and n be propositions where w is "I walk to work" b is "I work at Burger King" n is "I work at night" The sentence "When I work nights and I work at Burger King, I don't walk to work" could be written using propositions and logical connectives as:
(n Λ b) → ¬ w n → ¬ (w Λ b)
Assume that we are using the following system for storing real numbers. The system is defined as follows: bit 1: sign, 0 for positive, 1 for negative bits 2-9: exponent stored in excess-127 notation bits 10-32: mantissa In order to determine what a real number would look like in memory (according to this system) you first convert the value to binary, then normalize it and use the number of positions you moved the radix point as the exponent. Be sure you represent the exponent in excess-127 notation. What value does 0xC5900000 represent?
-100
Convert the following 2's compliment binary number to decimal: 10000111
-121
Convert the following 2's compliment binary number to decimal: 10000001
-127
Match the following two's complement, 8 bit numbers to their corresponding decimal numbers 11111110 10011110 11111111 10000000 01100111
-2 -98 -1 -128 103
Convert the following 2's compliment binary number to decimal: 10101111
-81
What is the fraction for the binary number .1101 ? .1101
.8125
812 % 2 (or, 812 mod 2) is:
0
Using two's compliment notation, convert 126 to decimal. Use 9 bits please.
001111110
Represent 112.75 as a 32-bit binary floating point number. Use 1 bit for the sign. Use 8 bits for the exponent, excess-127 notation. Use 23 bits for the mantissa.
01000010111000110000000000000000
Represent 12.5 as a 16-bit binary floating point number. Use 1 bit for the sign. Use 5 bits for the exponent, excess-15 notation. Use 10 bits for the mantissa.
0100101001000000
Assume that we are using the following system for storing real numbers. The system is defined as follows: bit 1: sign, 0 for positive, 1 for negative bits 2-6: exponent stored in excess-15 notation bits 7-16: mantissa In order to determine what a real number would look like in memory (according to this system) you first convert the value to binary, then normalize it and use the number of positions you moved the radix point as the exponent. Be sure you represent the exponent in excess-15 notation. What would 13.5 look like?
0100101011000000
Convert this decimal # to binary using 2's compliment, 8 bits: 78
01001110
Convert 2648 to binary
010110100
Convert this decimal # to binary using 2's compliment, 8 bits: 126
01111110
What is the biggest numeric value you can write in 8 bits using two's complement notation, using BINARY notation?
01111111
Convert -38.375 to 16 bit floating point format Sign, 1 bit. Exponent or characteristic - 5 bits in excess 15 notation 10 bit mantissa
0xD0CC
Convert the following 2's compliment binary number to decimal: 00000001
1
Match the following metric prefixes with their correct answer. Mega Giga Tera Kilo
1,000,000 1,000,000,000 1,000,000,000,000 1000
In converting a decimal number to binary, the result is 110110.11 When I normalize this number, what is the result?
1.1011011 x 2^5
Taking the decimal number -3.5 for conversion. Converting it to a 16-bit floating point number, 1 bit sign, 5 bit characteristic in excess-15 notation, 10 bit mantissa. The result is 0xC300 To convert the same number to a 32-bit floating point number, 1 bit sign, 8 bit characteristic i excess-127 notation, 23 bit mantissa. All you need to do is zero-fill the number on the right, or 0xC3000000 Is this true or false?
false
Match the following ˜ (3 > 2) ˜ (2 > 3)
false true
Match the following: if-then not or and
implication negation disjunction conjunction
Take the numbers m and n. I perform the operation m % n (m mod n) and the result is n=0. What can you tell me about m?
m is evenly divisible by n
Using DeMorgan's Law, ~p Λ q =
p V ~q
Which of the following is NOT a well defined set?
the set of ASU students with bad apartments
11011 2 + 10110 2 = 100011 2 is a statement
true
FF16 < 100 16 is a statement
true
Is the following implication true or false? If 3 * 2 = 6 then 5 > 4
true
Is the following implication true or false? If 3 * 2 = 7 then 4 + 3 = 8
true
Is the following true or false> ˜ (2>3)
true
Is the following true or false? 2 > 3 or 7 < 8
true
Is the following true or false? 3 > 2 and 7 < 8
true
Is the following true or false? 3 > 2 or 8 < 7
true
Observe the following truth table related to implications: p q p →q T T T T F F F T T F F T Consider the following statement: If the professor has a doctorate degree, then he can teach CS 1100. If the professor does NOT have a doctorate degree, then the implication is ___________?
true
C = {a: 1 < a <10, a is even} List all elements of C
{2,4,6,8}
Convert this decimal # to binary using 2's compliment, 8 bits: -113
10001111
Convert -55 to 7 bit 2's complement
1001001
Do the following addition problems in the base indicated: 1101010011 (binary) +110001111 -----------
10011100010
Convert the following hex value to binary: A4E57
1010 0100 1110 0101 0111
Convert the decimal number below to the base given: 327 (convert to binary)
101000111
Convert 21₁₀ to a binary (base 2) number. The answer is ________ .
10101 2|21-1 2|10-0 2|5-1 2|2-1 16 8 4 2 1 1 0 1 0 1
Convert ABCD16 to binary
1010101111001101
Perform the following addition: 0110012 + 0100012 ________
101010^2
Using two's compliment notation, convert -126 to binary. Use 9 bits please.
110000001
Represent -112.75 as a 32-bit binary floating point number. Use 1 bit for the sign. Use 8 bits for the exponent, excess-127 notation. Use 23 bits for the mantissa.
11000010111000110000000000000000
Convert -55 to 8 bit 2's complement
11001001
Convert 26.375 from decimal to binary
11010.011
Convert from decimal to two's compliment, 8 bits -10
11110110
Do the following subtraction problems in the base indicated: 2102100 (base-3) -212202 -------
1112121
Do the following subtraction problems in the base indicated: 20314 (hex) -EFDC -----
11338
Convert the decimal number 258 to an unsigned, binary number with 8 bits
8 bits is not enough to represent the number 258
Match the following terms with their correct definition Little endian Big endian
Data is stored with the most significant(higher) values last and least significant values first. Data is stored with the most significant(higher) values first and the least significant values last.
Convert the following number from the given base to decimal 2357 base 8 (octal)
1263
What is the biggest numeric value you can write in 8 bits using two's complement notation, written in decimal notation?
127
Do the following addition problems in the base indicated: 37675 (octal) +67545 -----------
127442
Convert the following to its metric prefix - 2^37
128 G
Convert 2^47 to the correct metric prefix.
128 T
Observe the following number: 1101 (this means 1101 base 2) What would this number be in base 10?
13
Convert the following number from the given base to decimal 20413 base 5
1358
Convert the following decimal number to octal - 12.184
14.136
Do the following addition problems in the base indicated: 52453 (base-6) +45524 -----------
142421
Four bit numbers act like mod __ numbers.
16
Convert 2^34 to a metric prefix
16 G
Convert 362.144 to hexadecimal. Carry your computation to three places after the radix (decimal)
16A.24D
Inside of computer memory, I found the following four characters: 43 2C 00 00 I thought it was the string "C,(null)(null)" But it turns out it was a 32 bit floating point number, 8 bits for the characteristic/exponent, excess-127 notation, 23 bit mantissa. What is this number?
172.0
(Q U R) ' = (Q' ∩ R') This is true because of the __________________ property
De Morgan
Convert binary to hexadecimal: 000111111011
1FB
Let A = { a, {} }. The cardinality of A is ___?
2
Do the following subtraction problems in the base indicated: 2102500 (octal) - 76754 -------
2003524
Convert the decimal number below to the base given: 1057 (convert to octal)
2041
Convert 138 from base 10 to base 8.
212^8
Convert the following number from the given base to decimal 34ABE base 16 (hexadecimal)
215742
How many bits do I need to store 23493287?
25
Observe the following number: 27₉ (this means 27 base 9) What would this number be in base 10?
25
Assume that we are using the following system for storing real numbers. The system is defined as follows: bit 1: sign, 0 for positive, 1 for negative bits 2-6: exponent stored in excess-15 notation bits 7-16: mantissa In order to determine what a real number would look like in memory (according to this system) you first convert the value to binary, then normalize it and use the number of positions you moved the radix point as the exponent. Be sure you represent the exponent in excess-15 notation. What value does 0100111100010000 represent?
28 1/4 or 28.25
Match the following answers for the binary number 010101010100111 Hexidecimal Octal
2AA7 25247
Express 224 using metric prefixes
2^45
At a local university department, 80 students were found to have owned a smartphone and a tablet computer. 70 students owned a smartphone. 43 students owned a tablet computer. How many students owned both a smartphone and a tablet computer?
33
Convert 2110 to a base 6 number. The answer is:
33 6|2110-3 6| 5- 216 36 6 1 13434
Convert 1111001 from binary to octal (base 8)
371
Convert 3310 to an octal (base 8) number. The answer is _______.
41 6356
Convert the following number from the given base to decimal: 101101 base 2 (binary)
45
Convert the decimal number below to the base given: 5 (convert to base-7)
5
How many bits minimum would you need to store the number 16 in binary, unsigned?
5
List five elements of the set {x | x=3k+5 and k is a natural number}.
5,8,11,14,17
What is the biggest number value we can express in 9 bits if we use unsigned numbers?
511
Which of the following is the hexadecimal representation of the phrase "Super Bowl" (you may ignore the ")
53 75 70 65 72 20 42 6F 77 6C
How many bits minimum would you need to store the number 16 in binary, signed?
6
Match the following numbers which are stated in standard scientific notation to expanded form (our usual way of writing decimal numbers). 6.5219 X 100 7.0001 X 106 3.427001 X 103
6.5219 7,000,100 3427.001
Convert 2^6 to the correct metric prefix.
64
Using metric prefixes, what is the largest 2's complement number you can store with 36 bits?
64G - 1
150 mod 13 (or, 150 % 13) is
7
Which of the following is the hexadecimal representation of the phrase "pepper" (you may ignore the ")
70 65 70 70 65 72
Convert 138 from base 10 to base 16 (hexadecimal).
8A^16
Convert 100101110101^2 to hexadecimal
975^16
Match the following 2 set Venn diagrams
A A intersect B A - B
In computer memory, I encounter the following hexadecimal values: 41 70 70 61 6C 61 63 68 69 61 6E 21 If I told you this was a character string, what do I have stored in these 12 values?
Appalachian!
Match the following number bases to their common names (some of these may NOT be in the text!)
Base 16: Hexadecimal Base 6: Senary, Heximal, Seximal Base 8: Octal Base 2: Binary Base 10: Decimal Base 5: Quinary, Pental
Match the following number systems terms with their correct answers. Binary Hexadecimal Decimal Octal
Base 2 Base 16 Base 10 Base 8
Let's start with the hexadecimal (base 16) number FFF. Match the correct number with the number base
Base 2: 11111111 Base 8: 7777 Base 10: 4095
Let's start with the decimal (base 10) number 224. Match the correct number with the number base
Base 8: 3406 Base 2: 11100000 Base 16: E0
A = {a,b,c,...,z} B = {a,c,e,...y} Which of the following is true?
B⊂A
Convert the decimal number below to the base given: 3225 (convert to hexadecimal)
C99
Convert -4.75 to 16-bit floating point with excess-15 notation.
Convert -4.75 to 16-bit floating point with excess-15 notation.
Convert 4.75 to 16-bit floating point with excess-15 notation.
Convert 4.75 to 16-bit floating point with excess-15 notation.
What is negation of the following statement? My favorite team is the Tigers
My favorite team is not the Tigers
Give the negation of: My wrist is sore and my elbow is sore
My wrist is not sore and my elbow is not sore
Which of the following is the power set for {2,4,6,8}?
P (A) = { {} , {2}, {4}, {6}, {8}, {2,4}, {2,6}, {2,8}, {4,6}, {4,8}, {6,8}, {2,4,6}, {2,4,8), {2,6,8,}, {4,6,8}, {2,4,6,8}} \)
Observe the following truth table: What does this represent?
P V Q
Let p = "I drink soft drinks" and q = "I eat beef" Using the logic symbols, match the following to their correct answers Either I drink soft drinks or I eat beef It is not true that I don't drink soft drinks or I don't eat beef I drink soft drinks and I do not eat beef
P V Q ~(~P V ~Q) P ∧ ~Q
Observe the following truth table: What does this represent?
P V ˜Q
Observe the following truth table: What does this represent?
P Λ Q
Find the power set of {a, {a}}.
P({a,{a}}) = {{ }, {a}, {{a}}, {a,{a}}}
Given A={1,2,4,5,7,9} and B={2,3,4,5,6}, match the following with their correct answer: A ∩ B A U B
{2,4,5} {1,2,3,4,5,6,7,9}
Which of the following is a proper subset of X = {2,4,6,8,10}?
{2,4,6}
The set U = {1,2,3,4,5,...,9} The set A = {1,3,5} The set B = {2,5,7,9} Match the following with their correct answers A ∩ B A U B (A U B)' A' A U B'
{5} [1,2,3,5,7,9} {4,6,8} {2,4,6,7,8,9} {1,3,4,5,6,8}
Observe the following truth table: p q ~p ~q ? T T F F F T F F T F F T T F F F F T T T What does this represent?
~ P Λ ~Q
The circuit on the performs an operation that is equivalent to:
¬ ((¬p Λ q)Vp) ¬ (pVq)
This is a truth table for:
¬Q, ¬P
I need at least 10 bits to store the integer 998.
True
Let A = { a, {} }. a is an element of A
True
Let A = { a, {} }. { {} } is a subset of A
True
Let A = { a, {} }. {a} is an element of A
True
Let A = { a, {} }. {} is an element of A
True
The mod function (%) divides two numbers and returns the remainder of the operation. So, if I perform 17 % 16, the mod is 1
True
The set G = {{1,2,3,4,5,6}} is a singleton set.
True
Match the following properties of sets A U X (where X is the universal set) A U Ø A ∩ Ø A ∩ A
X A Empty or null set A
Given the following set: A = {2,4,6,8,10) Which of the following are subsets of A?
a, c & d a. {2,6} c. {2,10} d. {4,2,8,6}
Match the following logic terms implication tautology biconditional contradiction
a->b true a<->b false
P ∩ Q = Q ∩ P This is true because of the __________________ property
commutative property of intersections
P U Q = Q U P This is true because of the __________________ property
commutative property of unions
If I have a statement x —> y , then match the following definitions: ~y -> ~x y - > x ~x -> ~y
contrapositive converse inverse
Match the following with their correct answers for the following statement: If I win the lottery, I am rich. If I am rich, I won the lottery If I am not rich, I did not win the lottery If I did not win the lottery, I am not rich
converse contrapositive inverse
P U (Q U R)= (P U Q) U R This is true because of the __________________ property
distributive
"What time is the football game Saturday?" is a statement
false
2 > 3 or 8 < 7
false
According to DeMorgan's Law (X U Y)' = X' U Y'
false
Is the following implication true or false? If 3 * 2 = 6 then 4 + 3 = 8
false
Is the following true or false> ˜ (3 > 2)
false
Is the following true or false? 2 > 3 and 7 < 8
false
Observe the following truth table related to implications: p q p →q T T T T F F F T T F F T Consider the following statement: If I am over 18 years of age, I can vote. If I am 26 years old and I cannot vote, then, the implication is ___________?
false
