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

Answers

Answer 1

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]


Related Questions

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

Answers

Answer:

a. Packets - Network layer

b. Segments - Transport layer

c. Bits - Physical layer

d. Frames - Data link layer

Explanation:

When TCP/IP protocols are used for communication between two network hosts, there is a process of coding and decoding also called encapsulation and decapsulation.

This ensures the information is not accessible by other parties except the two hosts involved.

Operating Systems Interconnected model (OSI) is used to standardise communication in a computing system.

There are 7 layers used in the OSI model:

1. Session Layer

2. Transport Layer

3. Network Layer

4. Data Link Layer

5. Physical Layer

6. Presentation layer

7. Application layer

The information formats given are matched as

a. Packets - Network layer

b. Segments - Transport layer

c. Bits - Physical layer

d. Frames - Data link layer

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.

Answers

Answer:

isn't it already showing it if not put text box

Explanation:

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