Question
In: Advanced Math
A binary string is a “word” in which each “letter” can only be 0 or 1...
A binary string is a “word” in which each “letter” can only be 0 or 1
Prove that there are 2^n different binary strings of length n.
Note:
- Your goal is to produce a properly constructed proof by induction, but this does not mean you have to follow
- Mathematical induction, step-by-step..
- Write the statement with n replaced by k
- Write the statement with n replaced by k+1.
- Identify the connection between the kth statement and the (k+1)th statement.
- Complete the induction step by assuming that the n=k version of the statement is true, and using this assumption to prove that the n=k+1 version of the statement is true.
- Complete the induction proof by proving the base case.
- point-by-point.
- ANOTHER IMPORTANT NOTE:
- Make sure you are addressing the given statement: "there are 2n different binary strings of length n” !!! So your solution should primarily be discussing binary strings. Yes, the fact that 2k+1 = 2k∙2 will be useful in your solution, but it should not be the sole content of your solution, as by itself that equality is a fact about exponents, not a fact about binary strings.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
A binary string is a “word” in which each “letter” can only be 0 or 1...
A binary string is a “word” in which each “letter” can only be 0
or 1
Prove that there are 2^n different binary strings of length
n.
Note:
Your goal is to produce a properly constructed proof by
induction, but this does not mean you have to follow
Mathematical induction, step-by-step..
Write the statement with n replaced by k
Write the statement with n replaced by k+1.
Identify the connection between the kth statement and the
(k+1)th statement.
Complete the...
A binary string is a “word” in which each “letter” can only be 0 or 1...
A binary string is a “word” in which each “letter” can only be 0
or 1
Prove that there are 2^n different binary strings of length
n.
Note:
Your goal is to produce a properly constructed proof by
induction, but this does not mean you have to follow
Mathematical induction, step-by-step..
Write the statement with n replaced by k
Write the statement with n replaced by k+1.
Identify the connection between the kth statement and the
(k+1)th statement.
Complete the...
A binary string is a “word” in which each “letter” can only be 0 or 1...
A binary string is a “word” in which each “letter” can only be 0
or 1
Prove that there are 2^n different binary strings of length
n.
Note:
Your goal is to produce a properly constructed proof by
induction, but this does not mean you have to follow
Mathematical induction, step-by-step..
Write the statement with n replaced by k
Write the statement with n replaced by k+1.
Identify the connection between the kth statement and the
(k+1)th statement.
Complete the...
1). The set of all string consisting of an uppercase letter followed by zero or more additional characters, each of which is either an uppercase letter or one of the digits 0 through 9.
For this problem, Give a BNF grammar for each of the descriptions below. show that you can get a number of positive examples of the language in the constructed grammar and also show that you are not able to get a set of negative examples in the grammar. Create a parse tree for the grammar after.
1). The set of all string consisting of an uppercase letter followed by zero or more additional characters, each of which is either an...
Assume that bits is a string that only contains the characters "0" and "1". n is...
Assume that bits is a string that only contains
the characters "0" and "1". n is an integer
variable that is less than the length of bits.
Fill in the blanks below to replace bits with a
new string that consists of all of the characters of
bits from index n through the
end, followed by the first n characters of
bits.
For example, if bits was "1101010" and
n was 3, the new value of bits
would be "1010110"....
Write a program that inputs a string that represents a binary number. The string can contain...
Write a program that inputs a string that represents a binary
number. The string can contain only 0s and 1s and no other
characters, not even spaces. Validate that the entered number meets
these requirements. If it does not, display an error message. If it
is a valid binary number, determine the number of 1s that it
contains. If it has exactly two 1s, display "Accepted". Otherwise,
display "Rejected". All input and output should be from the
console.
Examples of...
Convert the following values into binary numbers for each word and place the binary values in...
Convert the following values into binary numbers for each word
and place the binary values in
the two-dimensional array in their proper order of words.
Value
Binary Number Equivalent
Word 0
462,91210
Word 1
1142008
Word 2
5420h
Word 3
20,992d
Word 4
1104208
Word 5
6102008
Word 6
9F88h
Word 7
20,49610
Word 8
502416
Word 9
1101018
Word 10
71082h
Calculate the following 1) a. Give examples of each: A hex dword, a binary word, and...
Calculate the following
1) a. Give examples of each: A hex dword, a binary word, and
decimal byte
c. If x is a word, which command(s) are legal ?
movzx eax,x movzx ah,x movzx ax, x
d. How many bits in a word?
e. Put 12345h in DWORD format.
a) How many four-letter words can be formed from the letters of the word LAUNDRY if each...
a) How many
four-letter words can be formed from the letters of the word
LAUNDRY if each letter can only be used one time in a word? Y is
NOT considered a vowel in this word.
b) How many contain the letter
Y?
c) How many contain both
vowels?
d) How many of them contain
exactly three consonants?
e) How many of them begin and end
in a consonant?
f) How many begin with
N and end in a vowel?
g) How many begin with N and...
FIRST You are given a binary string x and an array A[1 : n] of binary...
FIRST You are given a binary string x and an
array A[1 : n] of binary strings. Assume that x and the elements of
A have the same length. Let ⊕ denote the xor operator on binary
strings. For example 1010 ⊕ 1101 = 0111, and 1110 ⊕ 1111 = 0001.
Assume that xor’ing two strings takes O(1) time. Give a
divide-and-conquer algorithm to check if there’s a subarray A[i :
j] of A such that A[i] ⊕ · ·...
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