Write all binary strings of length 4 (start with 0000 and end with 1111) in a co

Question

Write all binary strings of length 4 (start with 0000 and end with 1111) in a column and do the following:

(a) Explain why the number of binary strings of length 4 is 16.

(b) What would be the number of binary strings of length 7?

(c) On the rightside of each binary string of length 4 write m = #(1’s in the string).

(d) Use (c) to count the number of binary strings for each value of m = 0, 1, , 4; what do these numbers correspond to in terms of C(, )?.

(e) What is the sum of C(, )’s you obtained in (d)?

(f) Write the subsets of positions 1, 2, 3, and 4 to the left of each binary string of length 4.

Explanation / Answer

0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1

a)for each bit we have 2 options

and we have 4bits (length 4) so... 2*2*2*2 = 2^4 =16

b)binary strings of length 7 = 2^7 = 128

c)

0 0 0 0 0
0 0 0 1 1
0 0 1 0 1
0 0 1 1 2
0 1 0 0 1
0 1 0 1 2
0 1 1 0 2
0 1 1 1 3
1 0 0 0 1
1 0 0 1 2
1 0 1 0 2
1 0 1 1 3
1 1 0 0 2
1 1 0 1 3
1 1 1 0 3
1 1 1 1 4

d)

m number

0 1

1 5

2 5

3 4

4 1

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