Number Systems and Binary Code Quiz

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Questions and Answers

What does the numeral '11' represent in the binary numeral system?

Three (correct)

Twelve

Two

Eleven

In the decimal numeral system, which of the following values does the numeral '11' represent?

Eleven (correct)

Three

Twelve

Two

What is the least significant bit (LSB) in a binary number?

The bit that represents zero

The rightmost bit (correct)

The highest value bit

The leftmost bit

Which term describes the number that is added to another in an addition operation?

Addend Signup and view all the answers

What does binary code primarily consist of?

A series of 0s and 1s Signup and view all the answers

What defines a numeral system?

A way to write and express numbers using symbols Signup and view all the answers

In the context of numeral systems, what does the term 'radix' refer to?

The base of a system of numeration Signup and view all the answers

What is a bit in computer information?

Either the number 0 or 1 Signup and view all the answers

What is the hexadecimal equivalent of the binary number (110110.011101)2?

36.74 Signup and view all the answers

How do you convert an octal number to binary?

By writing the binary equivalent for each octal digit and combining them. Signup and view all the answers

Which of the following is the correct representation of (125)8 in binary?

001001010101 Signup and view all the answers

What is the first step in converting an octal number to hexadecimal?

Write the octal number's 3-bit binary equivalents. Signup and view all the answers

Which number is the binary equivalent of the hexadecimal number (25c.3af)16?

001001011100.001110101110 Signup and view all the answers

What is the result of converting (273.45)8 into hexadecimal?

0bb.94 Signup and view all the answers

What is the final step to convert binary to octal?

Group the binary digits into sets of three. Signup and view all the answers

What is a common mistake when converting from octal directly to hexadecimal?

Neglecting to convert to binary first. Signup and view all the answers

How is the decimal equivalent of a binary fraction calculated?

Multiply each bit by $2^{-n}$ where $n$ is the position from left to right. Signup and view all the answers

What is the value of the binary number (110101.0111) in decimal form?

53.4375 Signup and view all the answers

When converting a decimal number to hexadecimal, what conversion is necessary for remainders greater than 9?

They require alphabetic replacement. Signup and view all the answers

Which method is used to convert a binary number to octal?

Group the binary digits into groups of three. Signup and view all the answers

What is the hexadecimal equivalent of the decimal number 2479?

9A7 Signup and view all the answers

How is the result obtained when converting from decimal to binary?

By dividing the decimal number by 2 and tracking remainders. Signup and view all the answers

What is the significance of binary code in computer systems?

Binary code is the only language that computers understand. Signup and view all the answers

Which operation represents the correct conversion process when changing 286110 to hexadecimal?

Divide by 16, replace values greater than 9 with letters. Signup and view all the answers

Study Notes

Number Systems

Decimal System: The system we use in everyday life, it uses ten digits (0-9).
Binary System: The system computers use, using only two digits (0 and 1).
Unary System: A system that uses only one symbol (usually a single line) to represent a number.
Augend: The number to which another is added.
Addend: The number that is being added.
Radix (Base): The number of digits in a system.

Binary Code

Binary code is the most basic language computers understand.
Composed of series of 0s and 1s.
Used to represent numbers, letters, punctuation marks, and symbols.
Bit: The smallest piece of computer information, either 0 or 1.

Number System Conversion

Decimal to Binary: Divide the decimal number by 2 and record the remainder. Repeat until the result is 0. The remainders, read from bottom to top, form the binary equivalent.
Decimal to Hexadecimal: Divide the decimal number by 16 and note the remainder. Repeat until the quotient is 0. The remainders (converted to hexadecimal digits if greater than 9) form the hexadecimal number.

Binary to Other Number Systems

Binary to Decimal: Each binary digit is multiplied by a power of 2, starting from the rightmost digit as 2^0 and increasing for each position to the left. Add the results to obtain the decimal equivalent.
Binary to Octal: Divide the binary number into groups of 3 bits. Convert each group into its octal equivalent.
Binary to Hexadecimal: Divide the binary number into groups of 4 bits. Convert each group into its hexadecimal equivalent.

Octal to Other Number Systems

Octal to Binary: Convert each octal digit to its 3-bit binary equivalent and combine the results.
Octal to Hexadecimal: Convert the octal number into binary first, then group the bits into 4-bit groups and convert them into hexadecimal.

Hexadecimal to Other Number Systems

Hexadecimal to Binary: Convert each hexadecimal digit into its 4-bit binary equivalent and combine the results.
Hexadecimal to Octal: Convert the hexadecimal number to binary first, then group the bits into 3-bit groups and convert them into octal.

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Description

Test your knowledge on number systems, including decimal, binary, and unary. This quiz covers key concepts such as radix, augend, addend, and the conversion between decimal and binary codes. Perfect for students exploring the foundations of computer science.