Binary to Octal and Hexadecimal Conversion

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Questions and Answers

Which of the following correctly defines a number system?

A grouping of numbers used for graphic representations.

A framework for creating electronic devices.

A set of numbers that can perform one or more arithmetic operations. (correct)

A sequence of numbers used for counting only.

Which base does the octal number system use?

Base 2

Base 16

Base 8 (correct)

Base 10

What is the first step in converting binary to octal?

Group the binary digits into four from the right.

Convert each group directly to octal without modifications.

Pad the binary digits to three in order to group them. (correct)

Add 4, 2 and 1 underneath the binary numbers.

What is the primary characteristic of the binary number system?

It consists of only two symbols: 0 and 1. Signup and view all the answers

What is the binary equivalent of the octal number 123?

1100111 Signup and view all the answers

How many bits are in a byte?

Eight bits Signup and view all the answers

When converting the binary number 1010011 to decimal, what is the final value after adding the positional values represented by the binary 1's?

83 Signup and view all the answers

When converting binary 1010011 to hexadecimal, what is the correct grouping?

101|0011 Signup and view all the answers

After padding binary digits for hexadecimal conversion, what is the new binary grouping for 1010011?

0101|0011 Signup and view all the answers

In the hexadecimal number system, how is the number 12 represented?

C Signup and view all the answers

What is the sum of the octal values represented by 1’s in the binary 001010011?

6 Signup and view all the answers

Which digits are used in the decimal number system?

0 to 9 Signup and view all the answers

To convert binary to octal, how should the binary numbers be grouped?

In groups of three from the right Signup and view all the answers

What is the decimal equivalent of the binary number 1111001?

121 Signup and view all the answers

In the hexadecimal conversion of the binary number 1010011, what does the grouping represent?

53 Signup and view all the answers

Which value is the octal exponential value for the binary number 001010011 when converted to octal?

6 Signup and view all the answers

Which step is essential when converting a decimal number to binary?

Writing the decimal number as the dividend Signup and view all the answers

What does each remainder greater than 0 represent in binary conversion?

It represents the value 1. Signup and view all the answers

When converting from decimal to octal, what base is used for division?

8 Signup and view all the answers

During the conversion from decimal to hexadecimal, what operation is performed to find the remainder?

Subtract the given number from the quotient multiplied by 16. Signup and view all the answers

What is the final step in converting a number from decimal to binary?

Read the remainder values from bottom to top. Signup and view all the answers

In the octal to binary conversion process, how is each octal digit treated?

Individually converted to its binary equivalent. Signup and view all the answers

Which of the following statements is true regarding conversion to the binary system?

Only values of 0 and 1 are used. Signup and view all the answers

To convert a decimal to octal, what is the stopping condition for division?

When the quotient equals 0. Signup and view all the answers

Study Notes

Converting Binary Numbers to Octal

To convert a binary number to octal, first group the binary digits into groups of three, starting from the rightmost digit.
If the number of digits isn't a multiple of three, add leading zeros to make the last group have three digits.
Assign values of 4, 2, and 1 to the positions in each group (from left to right).
Octal values: Add the values where the binary digit is 1 and concatenate the results for each group.
Lastly, add the base "8" to indicate the octal value.

Converting Binary Numbers to Hexadecimal

Group the binary digits into groups of four, starting from the rightmost digit.
Pad with leading zeros if necessary to make the last group have four digits.
Assign values of 8, 4, 2, and 1 to the positions in each group (from left to right).
Hexadecimal values: Add the values where the binary digit is 1 and concatenate the results for each group.
Write the resulting number, with the base "16" indicating that it is a hexadecimal number.

Converting Decimal Numbers to Binary

Divide the decimal number by 2 repeatedly until you get a quotient of zero.
Write down the remainders (0 or 1) of each division as you go.
The remainders, read from bottom to top, form the binary representation of the decimal number.

Converting Decimal Numbers to Octal

Divide the decimal number by 8 repeatedly until you get a quotient of zero.
Write down the remainders of each division.
Read the remainders from bottom to top to obtain the octal representation of the decimal number.

Converting Decimal Numbers to Hexadecimal

Divide the decimal number by 16 repeatedly, recording the remainders as you go.
Convert any remainders greater than 9 to their hexadecimal equivalent (A=10, B=11, C=12, D=13, E=14, F=15).
Read the remainders from bottom to top to obtain the hexadecimal representation of the decimal number.

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Description

This quiz explores the methods for converting binary numbers to octal and hexadecimal formats. It covers the grouping techniques needed to effectively convert binary digits, including how to handle leading zeros. Test your understanding of these important number systems.