CS-1100 Discrete Math

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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


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