How many bit strings of length 8 if i. bit strings start with
the bit 1; ii. bit strings end with the two bits 00; iii. bit
strings either start with the bit 1 or end with the bits 00.؟
1. How many 12-bit strings (that is, bit strings of length 14)
start with the sub-string 011?
2. You break your piggy bank to discover lots of pennies and
nickels.
You start arranging them in rows of 6 coins.
How many coins would you need to make all possible rows of 6
coins (not necessarily with equal numbers
of pennies and nickels)?
3. How many shortest lattice paths start at (4, 4) and end at
(13, 13)?
4. What is...
find a
recurrence relation for the number of bit strings of length n that
contain the string 10. What are the initial conditions? How many
bit strings of length eight contain the string 10
find a
recurrence relation for the number of bit strings of length n that
contain two consecutive 1s. What are the initial conditions? How
many bit strings of length eight contain two consecutive
1s
1. Provide a regular expression that describes all bit-strings
that length is at least one and at most three.
2. Provide a regular expression that describes all bit strings
with odd length.
Recall that a 5-bit string is a bit strings of length
5, and a bit string of weight 3, say, is one with exactly three
1’s.
a. How many 5-bit strings are there?
b. How many 5-bit strings have weight 0?
c. How many 5-bit strings have weight 1?
d. How many 5-bit strings have weight 2?
e. How many 5-bit strings have weight 4?
f. How many 5-bit strings have weight 5?
g. How many 5-bit strings have weight...