Test: Number system and Encoding Schemes - Grade 11 MCQ

ASCII stands for American Standard Code for Information Interchange,
Key Points
ASCII is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices

• The original ASCII was a 7-bit character set (128 possible characters) 
• Currently used ASCII is an 8-bit code. That is, it uses eight bits to represent a letter or a punctuation mark.
• Character sets used today are generally 8-bit sets with 256 different characters, effectively doubling the ASCII set.

• To calculate the time it will take to download a movie of 16 gigabytes with a download speed of 64 megabytes per second, we first need to convert both the movie size and the download speed to the same units.
• Since 1 gigabyte is equal to 1024 megabytes, we have:
• 16 gigabytes = 16 x 1024 megabytes = 16384 megabytes
• If 64 megabytes are downloaded in 1 sec

16384 megabytes (16gigabytes) will be downloaded in 16384/64=256 sec
So, it will take 256 seconds to download a 16 gigabyte movie at a download speed of 64 megabytes per second.

The binary system uses two symbols 0 and 1. 
Key Points
Statement I: The binary equivalent of decimal number (19)₁₀ is (10101)₂.

• To convert the binary equivalent of a decimal number 
  • ​19/2 = 1
  • 9/2 = 1
  • 4/2 = 0 
  • 2/2 = 0
  • 1/2 = 1
• So, (19)₁₀ = (11001)₁₀

Hence, Statement I is false. 
Statement II: (1011)₂ + (110)₂ = (10101)₂

• (1011)₂ + (110)₂ = (10101)₂

​LHS

• (1011)₂ = 1. 2⁴ + 0. 2³ + 1.2² + 1.2⁰ = (22)₁₀
• (110)₂ = 1.2³ +1.2² + 0.2¹ = (12)₁₀

RHS

• (10101)2 = 1.2⁵ + 0.2⁴ + 1.2³ + 0.2² + 1.2¹ = (42)₁₀
• Now, (22)₁₀ + (12)₁₀ = (34)₁₀ 

LHS is not equal to RHS

• Therefore, (34)₁₀ is not equal to (42)₁₀

So, Statement II is false. 
Therefore, Both Statement I and Statement II are false. 

Statement I: 8 megabytes = 2¹³ gigabytes. 

• As we know, 1 MB = 20¹⁰ KB. 
• So, 8 MB = 2³ + 20¹⁰ KB
• Thus, 8 MB = 2¹³ KB 

Thus, Statement I is false. 
Statement II: The decimal equivalent of the binary number (11101.101)₂ is (29.625)₁₀.

• According to Question, (11101.101)2 = (29.625)10.
• Now, Convert the Binary number to a Decimal number, 
  • ​(11101.101)2  = 1*24+1*23+1*22 + 0*21+1*20. 1*2-1+0*2-2+1*2-3 
  • (11101.101)2 = 16+8+4+0.1/2+1/8. 
  • (11101.101)2 = 29 (·500+·125). 
  • (11101.101)2 = 29 (·625)
  • ​Thus, (11101.101)2 = 29.625

So, Statement II is true. 
Therefore, The correct answer is  Statement I is false but Statement II is true.

Hexa-Decimal number systems use the A-F system.
Key Points
The following table will discuss the four number system, 

• In most computer systems, a byte is an eight binary digit long unit of data.
• Most computers use a unit called a byte to represent a character, such as a letter, number, or typographic sign.
• Each byte can be used to hold a string of bits that must be combined into a larger unit for application needs.
• 8 bits make up the binary number 11000101.
• The binary number 11000101 has 1 byte since it has 8 bits.

A number system includes the number of independent digits used in the number system (the base), the place values of the different digits constituting the number and the maximum numbers that can be written with the given number of digits.
The Binary Number System:

• A computer system uses bits (binary digits) to denote values. It uses the binary number system to store data.
• Each digit (0 or 1) is a bit thus the binary number 10110110 is a binary number having 8 bits.
• The binary number system with only two independent digits, 0 and 1, is a base-2 number system. All larger binary numbers are represented in terms of ‘0’ and ‘1’.
• A binary number can easily be converted to a decimal by multiplying each digit by a power of 2.

NOTE:

• The decimal number system has a base of 10 as it has 10 independent digits, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
• The hexadecimal number system uses 16 symbols (base 16) which includes numbers from 0 to 9 and letter A to F. A nibble is one digit of a hexadecimal value which represents 4 bits.
• The octal number system use base 8. Octal numbers are written using digits 0 through 7.

Hence, it is clear from the given points that a computer uses the binary number system to store data and perform calculations.

The number system is a way to represent or express numbers. You have heard of various types of number systems such as the whole numbers and the real numbers. But in the context of computers, we define other types of number systems. They are:

• The decimal number system
• The binary number system
• The octal number system and
• The hexadecimal number system

Key-Points
Binary Number System:

• A binary number system is one of the four types of number system. 
• In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one). 
• The binary numbers here are expressed in the base-2 numeral system. 
• For example, (101)2 is a binary number. Each digit in this system is said to be a bit.

Here we will show you step-by-step how to convert the decimal number 35 to binary.

• Step 1) Divide 35 by 2 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.
• Step 2) Divide the Whole part of the Quotient from Step 1 by 2. Again, keep the Whole part and set the Remainder aside.
• Step 3) Repeat Step 2 above until the Whole part is 0.
• Step 4) Write down the Remainders in reverse order to get the answer to 35 as a binary.

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression that uses only two symbols: typically "0" (zero) and "1" (one).
Key Points
Statement I: The base of the binary number system is 2.
Explanation: 

• Binary is a number system comprised of two digits, 0 and 1, used by computers to represent all other numbers and characters.
• So, Binary is also known as base 2.
• Binary is a base-2 number system invented by Gottfried Leibniz that's made up of only two numbers or digits: 0 (zero) and 1 (one).
• This numbering system is the basis for all binary code, which is used to write digital data such as the computer processor instructions used every day.

So, we can say that statement I is true.
Statement II: Binary addition is just like decimal addition except that the rules are much simpler.

Explanation: 

• Binary addition is one of the binary operations.
• The binary addition operation works similarly to the base 10 decimal system, except that it is a base 2 system.
• There are 3 basic rules for adding binary numbers:
  • 0 + 0 = 0
  • 0 + 1 = 1
  • 1 + 1 = 10. If the sum of 2 bits is greater than 1, we need to shift a column on the left.
• In decimal system, 1 + 1 = 2. Binary notation of 2 is 10 (1 * 2^1 + 0 * 2^0). So we keep 0 in the 1's column and shift (carry over) 1 to the 2's column.

So, we can say that Statement II is also correct.
Therefore, both Statement I and Statement II are true.

In decimal to binary conversion, we convert a base 10 number to a base 2 number by using simple methods. For example, if 1210 is a decimal number then its equivalent binary number is 11002.
Key Points
Converting 67.625₁₀ in Binary system here so:
The whole part of a number is obtained by dividing on the basis of new

Happened :67₁₀ = 10000112
The fractional part of the number is found by multiplying on the basis of new

Happened:0.625₁₀ = 0.1012
Add up together whole and fractional part here so:
10000112 + 0.1012 = 1000011.1012
Result of converting:
67.625₁₀ = 1000011.1012
Hence the binary equivalent of the decimal number 67.625 is 1000011.1012.

A number system includes the number of independent digits used in the number system (the base), the place values of the different digits constituting the number and the maximum numbers that can be written with the given number of digits.
The Binary Number System: The binary number system with only two independent digits, 0 and 1, is a base-2 number system. All larger binary numbers are represented in terms of ‘0’ and ‘1’.
Decimal to Binary Conversion:
Step 1: Divide 75 by 2 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.
75 / 2 = 37 with 1 remainder
Step 2: Divide the Whole part of the Quotient from Step 1 by 2. Again, keep the Whole part and set the Remainder aside.
37 / 2 = 18 with 1 remainder
Step 3: Repeat Step 2 above until the Whole part is 0.
18 / 2 = 9 with 0 remainder
9 / 2 = 4 with 1 remainder
4 / 2 = 2 with 0 remainder
2 / 2 = 1 with 0 remainder
1 / 2 = 0 with 1 remainder
Step 4: Write down the Remainders in reverse order to get the answer to 75 as a binary.
When we put the remainders together in reverse order, we get the answer 1001011
Hence, the binary equivalent of decimal number 75 is 1001011
NOTE:
The decimal number system has a base of 10 as it has 10 independent digits, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The octal and hexadecimal number systems have a radix (or base) of 8 and 16, respectively.

Computer work in binary digits, 0 and 1, called bits. Most computers can process millions of bits every second. Different types of data require different amounts of storage space.

Hence, from the given table it is clear that one Terabyte (TB) of memory is equal to 1024 × 1024 × 1024 KB.

A number system includes the number of independent digits used in the number system (the base), the place values of the different digits constituting the number, and the maximum numbers that can be written with the given number of digits.
The Binary Number System: 

• The binary number system with only two independent digits, 0 and 1, is a base-2 number system.
• All larger binary numbers are represented in terms of ‘0’ and ‘1’.

Key Points

• The number of 8-bit strings beginning with 111 is 32.The 
• First 3 bits are fixed and the remaining 5 bits can be 0 or 1.
• So the total combinations are 25=32
• The same is the case with the strings starting with 101.
• So the total number of strings is 32+32=6432+32=64" role="presentation" style="display: inline; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">32+32=64.

Hence, the number of 8-bit strings that can be formed beginning with either “111...” or “101...” is 64.

• The amount of data that can be stored in a storage unit is known as a memory unit.
• A binary digit or 'bit' is the representation of '0' and '1' is considered as the smallest unit of memory.
• A group of binary digits (8 bit) called byte.

Key-Points
The table below is showing the memory units and their equivalents:

Therefore, from the above information, the correct pair is 1 Megabyte = 10⁶.

Five-bit Communications Protocol (FCP):

• The Five-bit Communications Protocol (FCP) is a method of communicating, which uses two states (expressed as '1' and '0') to represent characters in fixed five-bit code sizes and also defines a standard procedure for transmissions.
• This protocol is designed to be easily retained in memory.
• It can also, however, be used to send and receive transmissions effectively without requiring complete memorization of the codes by following a written reference sheet.
• The character sets can easily be recreated and written down on a sheet of paper with a minimal amount of memorization of the patterns in the character sets.
• This protocol can be used to communicate between two persons provided there is some way to represent two distinct states (expressed as '1' and '0') to send the five-bit characters.