let m be a positive integer with n bit binary representation an-1 an-2 ... a1a0 with an-1=1 what are the smallest and largest values that m could have

Answer:

Explanation:

From the given information:

[tex]a_{n-1} , a_{n-2}...a_o[/tex] in binary is:

[tex]a_{n-1}\times 2^{n-1} + a_{n-2}}\times 2^{n-2}+ ...+a_o[/tex]

So, the largest number posses all [tex]a_{n-1} , a_{n-2}...a_o[/tex]  nonzero, however, the smallest number has [tex]a_{n-2} , a_{n-3}...a_o[/tex] all zero.

∴

The largest = 11111. . .1 in n times and the smallest = 1000. . .0 in n -1 times

i.e.

[tex](11111111...1)_2 = ( 1 \times 2^{n-1} + 1\times 2^{n-2} + ... + 1 )_{10}[/tex]

[tex]= \dfrac{1(2^n-1)}{2-1}[/tex]

[tex]\mathbf{=2^n -1}[/tex]

[tex](1000...0)_2 = (1 \times 2^{n-1} + 0 \times 2^{n-2} + 0 \times 2^{n-3} + ... + 0)_{10}[/tex]

[tex]\mathbf {= 2 ^{n-1}}[/tex]

Hence, the smallest value is [tex]\mathbf{2^{n-1}}[/tex] and the largest value is [tex]\mathbf{2^{n}-1}[/tex]

Given that the variable named Boy = "Joey" and the variable named Age = 6, create statements that will output the following message:

Congratulations, Joey! Today you are 6 years old.

First, write one statement that will use a variable named Message to store the message. (You will need to concatenate all of the strings and variables together into the one variable named Message. If you don't know what that means, read the section in Chapter 1 about concatenation.)
Then write a second statement that will simply output the Message variable.

During TCP/IP communications between two network hosts, information is encapsulated on the sending host and decapsulated on the receiving host using the OSI model. Match the information format with the appropriate layer of the OSI model.

a. Packets
b. Segments
c. Bits
d. Frames

1. Session Layer
2. Transport Layer
3. Network Layer
4. Data Link Layer
5. Physical Layer