How many 14-bit strings (that is, bit strings of length 14) are there with: (a) start with sub-string 011? (b) have weight 7 (i.e., contain exactly 7 1’s) and start with the sub-string 011? (c) either start with 011 or end with 01 (or both)? (d) have weight 7 and either start with 011 or end with 01 (or both)?

How many length eight binary strings (strings with eight characters, each of which is “0” or “1”)start with “111”? How many length eight binary strings contain exactly one zero?

write an encoder and a decoder for a modified "book cipher." A book cipher uses a document or book as the cipher key, and the cipher itself uses numbers that reference the words within the text. For example, one of the Beale ciphers used an edition of The Declaration of Independence as the cipher key. The cipher you will write will use a pair of numbers corresponding to each letter in the text. The first number denotes the position of a word in the key text (starting at 0), and the second number denotes the position of the letter in the word (also starting at 0). For instance, given the following key text (the numbers correspond to the index of the first word in the line)   [0] 'Twas brillig, and the slithy toves Did gyre and gimble in the wabe; [13] All mimsy were the borogoves, And the mome raths outgrabe. [23] "Beware the Jabberwock, my son! The jaws that bite, the claws that catch! [36] Beware the Jubjub bird, and shun The frumious Bandersnatch!" [45] He took his vorpal sword in…

A What bit string represents the bitwise OR of bit strings 0110 and 1110?  B What is the difference of these sets, i.e., {1,3,4} - {2,3,5}?   C What is the value of x after this statement is encountered in a computer program, if x = 1 before the statement is reached? if x + 1 < 3 then x := x + 1 D What is the union of sets {1,3,4} and {2,3,5}? E What is the cartesian product of sets {1,3,4} and {2,9}? F Let U={0,1,2,3,4,5,6,7}. What bitstring represents the subset of all odd integers in U? G What is the powerset of set {1,3,4}? H What bit string represents the bitwise AND of bit strings 0110 and 1110? I What is the intersection of sets {1,3,4} and {2,3,5}?

Find the decimal values of the following signed (negative) numbers. First find a signed-magnitude binaryrepresentation for them and then convert them to decimal numbers: a. (71)8= (111001)2 signed-magnitude =b. (80C)16 = (100000001100)2 signed-magnitude =c. (10100101)2 = (-0100101)2 signed-magnitude =

I need to solve the following: "ii) Suppose a book has the ISBN number 0444x50090, where the digit represented by x has been lost in transmission. What is x?" I know that for encoding there's a formula one can use but I'm confused about how to use it with the x?

Consider all bit (binary digit) strings of length 12. How many begin with 110? How many begin with 11 and end with 10? How many begin with 11 or end with 10? How many have exactly four 1s?

Let's count ternary digit strings, that is, strings in which each digit can be 0, 1, or 2. a. How many ternary digit strings contain exactly ʼn digits? b. How many ternary digit strings contain exactly n digits and n 2's. c. How many ternary digit strings contain exactly n digits and n - 1 2's. (Hint: where can you put the non-2 digit, and then what could it be?) d. How many ternary digit strings contain exactly n digits and n - 2 2's. (Hint: see previous hint) e. How many ternary digit strings contain exactly n digits and n – k 2's. f. How many ternary digit strings contain exactly n digits and no 2's. (Hint: what kind of a string is this?) g. Use the above parts to give a combinatorial proof for the identity (1) + ²(7) + 2² (2) + 2³ (3) +... 2² (1) +2 = 3¹. =

W02 Q8. strings are there that each have the same bit string appearing in positions 4 through 13 (inclusive)? A 32-bit string has digit positions numbered from 0 to 31. How many 32-bit