Number Theory Test 11

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Number Theory Test 11

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Question 1
1 / -0

Which of the following is a prime number?

A
$$19$$

B
$$20$$

C
$$21$$

D
$$22$$

Solution

Prime number is a number which has 1 and number it self as a factor.

19=1$$\times $$19 (or) 19$$\times $$1

20=2$$\times $$10 (or) 20$$\times $$1 (or) 5$$\times $$4

21 = 21$$\times $$1 (or) 7$$\times $$3

22=1$$\times $$22 (or) 11$$\times $$2

So, 19 is prime number
Question 2
1 / -0

Which of the following is not a prime number?

A
$$23$$

B
$$29$$

C
$$43$$

D
$$21$$

Solution

Factors of $$23 = 23 \times 1$$
Factors of $$29 = 29 \times 1 $$
Factors of $$43 = 43 \times 1$$
Factors of $$21 = 3 \times 7$$
So, ioption D $$23$$ is not a prime number
Question 3
1 / -0

Instructions and memory address are represented by

A
Character code

B
Binary codes

C
Binary word

D
parity bit

Solution

Instructions and memory address are represented by Binary codes.

ASCII code. The American Standard Code for Information Interchange (ASCII), uses a 7-bit binary code to represent text and other characters within computers, communications equipment, and other devices. Each letter or symbol is assigned a number from 0 to 127.

A bit (short for binary digit) is the smallest unit of data in a computer. A bit has a single binary value, either 0 or 1. Although computers usually provide instructions that can test and manipulate bits, they generally are designed to store data and execute instructions in bit multiples called bytes.
Question 4
1 / -0

Bit stands for

A
Binary digits

B
bit of system

C
a part of byte

D
All of above

Solution

Bit stands for Binary digits

A bit (short for binary digit) is the smallest unit of data in a computer. A bit has a single binary value, either 0 or 1. Although computers usually provide instructions that can test and manipulate bits, they generally are designed to store data and execute instructions in bit multiples called bytes.

Binary (or base-2) a numeric system that only uses two digits — 0 and 1. Computers operate in binary, meaning they store data and perform calculations using only zeros and ones. A single binary digit can only represent True (1) or False (0) in boolean logic.

A bit (short for binary digit) is the smallest unit of data in a computer. A bit has a single binary value, either 0 or 1. Although computers usually provide instructions that can test and manipulate bits, they generally are designed to store data and execute instructions in bit multiples called bytes.
Question 5
1 / -0

The roots of the equation $${ \left( z+\alpha \beta \right) }^{ 3 }={ \alpha }^{ 3 }$$ represent the vertices of a triangle, one of whose sides is of length

A
$$\sqrt { 3 } \left| \alpha \beta \right|$$

B
$$\sqrt { 3 } \left| \alpha \right|$$

C
$$\sqrt { 3 } \left| \beta \right|$$

D
$$None\ of\ these$$

Solution

$$z_1=\alpha-\alpha \beta,z_2=\alpha\omega-\alpha \beta,z_3=\alpha\omega^2-\alpha \beta$$
Let vertices be denoted by $$A,B,C$$
Length of $$AB=|z_1-z_2|=|\alpha||1-\omega|=|\alpha|\left|1-\dfrac{-1-i\sqrt{3}}{2}\right|=\sqrt{3}|\alpha|$$
Length of $$BC=|z_2-z_1|=|\alpha|\left|1-\dfrac{-1+i\sqrt{3}}{2}\right|=\sqrt{3}|\alpha|$$
Length of $$BC=|z_3-z_1|=|\alpha||\omega|\left|\dfrac{-1+i\sqrt{3}}{2}\right|\left|1-\dfrac{-1+i\sqrt{3}}{2}\right|=\sqrt{3}|\alpha|$$
Hence option B is correct.
Question 6
1 / -0

A byte is made up of

A
Eight bytes

B
Eight binary digits

C
Two binary digits

D
Tow decimal points

Solution

A byte is made up of Eight binary digits.

A byte consists of 8 adjacent binary digits (bits), each of which consists of a 0 or 1. The string of bits making up a byte is processed as a unit by a computer; bytes are the smallest operable units of storage in computer technology. byte.

8 bits, can represent positive numbers from 0 to 255. hexadecimal. A representation of 4 bits by a single digit 0..9,A..F. In this way a byte can be represented by two hexadecimal digits.

Binary number. In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit.
Question 7
1 / -0

How many options doe a BINARY choice offer

A
None

B
One

C
Two

D
it depends on the amount of memory on the computer

E
It depends on the speed of the computer's processor

Solution

Two options doe a BINARY choice offer.

Binary (or base-2) a numeric system that only uses two digits — 0 and 1. Computers operate in binary, meaning they store data and perform calculations using only zeros and ones. A single binary digit can only represent True (1) or False (0) in boolean logic.

Binary in Digital Computers and Electronic Devices. Numbers can be encoded in binary format and stored using switches. ... In a computer, switches are implemented using transistors. The smallest memory configuration is the bit, which can be implemented with one switch.

Binary number. In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit.
Question 8
1 / -0

Which number system is usually followed in a typical 32-bit computer?

A
Binary

B
Decimal

C
Hexadecimal

D
Octal

Solution

Binary number system is usually followed in a typical 32-bit computer.

A binary number system is usually followed in a 64-bit computer. A binary number system is usually followed in a 64-bit computer. 2 number system is usually followed in a typical 32-bit computer.

Binary number. In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one). The base-2 numeral system is a positional notation with a radix of 2.
Question 9
1 / -0

............... code is used to implement data transparency in the binary synchronous protocol.

A
$$DLE$$

B
$$NAK$$

C
$$EOH$$

D
$$EOT$$

Solution

DLE code is used to implement data transparency in the binary synchronous protocol.

When it is possible that frame delimiting characters may appear in the data then it is necessary to provide data transparency; ie the data must be ignored by the frame synchronisation system. An example of this would be in a character oriented protocol when a “binary” file was being transmitted; eg a compiled program. It could easily contain the ETX code somewhere within the file. In this case character (or byte) stuffing (or more formally DLE insertion) is used to achieve data transparency.

This method precedes the “true” STX or ETX characters with a data link escape (DLE) code. Then the transmitter inserts (stuffs) a DLE before every DLE it finds in the data. The receiver knows (by receiving a DLE-STX) that data transparency is in operation. If later in the frame it finds two DLEs in sequence it will destuff (ie delete one of them) and pass the second as data. It will therefore recognise the true end of frame (the only single DLE followed by an ETX).

Binary Synchronous Communication (BSC or Bisync) is an IBM character-oriented, half-duplex link protocol, announced in 1967 after the introduction of System/360. It replaced the synchronous transmit-receive (STR) protocol used with second generation computers. The intent was that common link management rules could be used with three different character encodings for messages. Six-bit Transcode looked backwards to older systems; USASCII with 128 characters and EBCDIC with 256 characters looked forward. Transcode disappeared very quickly but the EBCDIC and USASCII dialects of Bisync continued in use.
Question 10
1 / -0

Put the following in the form of A + iB :
$$\dfrac{(3 \, - \, 2i)(2 \, + \, 3i)}{(1 \, + \, 2i)(2 \, - \, i)}$$

A
$$\dfrac{3}{4} \, + \, \dfrac{9}{4} \, i$$

B
$$\dfrac{63}{25} \, - \, \dfrac{16}{25} \, i$$

C
$$\dfrac{5}{4} \, + \, \dfrac{9}{4} \, i$$

D
$$\dfrac{1}{4} \, + \, \dfrac{7}{4} \, i$$

Solution

$$\cfrac{(3-2i)(2+3i)}{(1+2i)(2-i)}$$
$$\implies \cfrac{6+9i-4i+6}{2-i+4i+2}$$
$$\implies \cfrac{12+5i}{4+3i}$$
$$\implies \cfrac{(12+5i)(4-3i)}{4^2+3^2}$$
$$\implies \cfrac{48-36i+20i+15}{25}$$
$$\implies \cfrac{63}{25}$$$$-i \cfrac{16}{25}$$

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Number Theory Test 11

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Number Theory Test 11

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SHARING IS CARING

Question 1

$$19$$

$$20$$

$$21$$

$$22$$

Solution

Question 2

$$23$$

$$29$$

$$43$$

$$21$$

Solution

Question 3

Character code

Binary codes

Binary word

parity bit

Solution

Question 4

Binary digits

bit of system

a part of byte

All of above

Solution

Question 5

$$\sqrt { 3 } \left| \alpha \beta \right|$$

$$\sqrt { 3 } \left| \alpha \right|$$

$$\sqrt { 3 } \left| \beta \right|$$

$$None\ of\ these$$

Solution

Question 6

Eight bytes

Eight binary digits

Two binary digits

Tow decimal points

Solution

Question 7

None

One

Two

it depends on the amount of memory on the computer

It depends on the speed of the computer's processor

Solution

Question 8

Binary

Decimal

Hexadecimal

Octal

Solution

Question 9

$$DLE$$

$$NAK$$

$$EOH$$

$$EOT$$

Solution

Question 10

$$\dfrac{3}{4} \, + \, \dfrac{9}{4} \, i$$

$$\dfrac{63}{25} \, - \, \dfrac{16}{25} \, i$$

$$\dfrac{5}{4} \, + \, \dfrac{9}{4} \, i$$

$$\dfrac{1}{4} \, + \, \dfrac{7}{4} \, i$$

Solution

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