Converting Decimal Fractions to Base 5

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What is the first step in converting the fractional part of a decimal number to another base?

Group the deducted integers.

Deduct the integer part from the product.

Multiply the fraction by the base. (correct)

Repeat the process until the fraction is zero.

What should be done with the integer part obtained during the conversion process?

It should be kept aside for later use. (correct)

It should be added to the new value.

It should be converted back to decimal.

It should be ignored completely.

When do you stop the conversion process of the fractional part?

When the integer part becomes too large.

When a rounded number is achieved.

When the base has been reached.

When the remaining fraction is zero or enough digits are obtained. (correct)

What is the final step after obtaining several integer parts during conversion?

Group the deducted integers from top to bottom. Signup and view all the answers

If you want to convert a decimal fraction to base 5, how will the first integer be determined?

By multiplying the fraction by 5. Signup and view all the answers

What is the first integer result when converting 0.430410 to base 5?

2 Signup and view all the answers

How many multiplication steps are required before reaching a fractional part of zero when converting 0.430410 to base 5?

Three Signup and view all the answers

What is the final base 5 representation of the decimal fraction 0.430410?

0.20345 Signup and view all the answers

What would be the result of the second multiplication step (0.1520 × 5) during the conversion process?

0.7600 Signup and view all the answers

What base is being used in the conversion of 0.430410?

Base 5 Signup and view all the answers

What is the second bit in the binary representation of 0.3437510 when converted to binary?

1 Signup and view all the answers

Which operation is performed to convert the fractional part of a decimal number to binary?

Multiply by 2 Signup and view all the answers

In converting 0.3437510 to binary, what fractional value is derived after the fourth multiplication?

0.75000 Signup and view all the answers

What is the correct binary representation of 0.3437510 up to 4 bits to the right of the binary point?

0.01012 Signup and view all the answers

After the first multiplication of 0.34375 by 2, what integer part is produced?

0 Signup and view all the answers

What is the first step when converting a number from any base to decimal?

Multiply each digit by the base raised to the power of its position Signup and view all the answers

When converting from base n to decimal, what power should the least significant bit (LSB) have?

0 Signup and view all the answers

What should you do after multiplying each digit by the base raised to its power?

Add all the intermediate results together Signup and view all the answers

How are the positions of digits after the decimal point treated when converting to decimal?

They have negative powers starting from -1 Signup and view all the answers

If you have a number in base 4 represented as '312', what is the value of the digit '3' in decimal?

12 Signup and view all the answers

What method is used to convert the fractional part from decimal to another base?

Multiplication by the base and taking the integer part Signup and view all the answers

Why do we use multiplication instead of the remainder method for fractional parts?

Because fractions are expressed in negative powers of the base Signup and view all the answers

In a base conversion, what is the significance of the integer part obtained from the multiplication process?

It represents the new fractional part in the target base Signup and view all the answers

Which of the following best describes how fractions in decimal are expressed when converted to another base?

Using only negative powers Signup and view all the answers

Which of the following is an example of a fraction in base 10?

2390167.1208 Signup and view all the answers

What is the primary relationship between octal and binary systems?

Each octal digit corresponds to a group of 3 binary digits. Signup and view all the answers

What is the grouping size for converting binary to hexadecimal?

4 binary digits per hexadecimal digit. Signup and view all the answers

Which of the following statements is true regarding binary conversions?

Binary numbers can be converted directly to octal and hexadecimal. Signup and view all the answers

Which base is equivalent to hexadecimal in terms of power-of-two notation?

Base 16 Signup and view all the answers

If 11101100 is split for hexadecimal conversion, which grouping is correct?

1110 1100 Signup and view all the answers

What is the decimal equivalent of the binary number 10.11?

2.75 Signup and view all the answers

What is the value of the letter 'A' in hexadecimal when converting to decimal?

10 Signup and view all the answers

When converting the hexadecimal number 1A.5 to decimal, what is the contribution of the digit '5'?

0.3125 Signup and view all the answers

If you convert the hexadecimal number 2F.3 to decimal, what is the contribution of the digit '2'?

16 Signup and view all the answers

For the binary number 110.101, what is the total final value when converted to decimal?

6.5 Signup and view all the answers

What is the first step in converting the Hex number 351B to Octal?

Convert Hex to Binary Signup and view all the answers

After converting Hex to Binary, how are the binary bits grouped for the conversion to Octal?

In sets of three bits Signup and view all the answers

Which binary value represents the Hex digit 'B' during conversion?

1010 Signup and view all the answers

What is the Octal equivalent of the Hex number 351B after completing the conversion?

32433 Signup and view all the answers

Why is it useful to convert through Binary when changing from Hex to Octal?

It ensures accuracy in converting between bases. Signup and view all the answers

What is the primary reason for converting a number to base 10 when changing bases?

It simplifies the conversion process. Signup and view all the answers

Which scenario is an exception to the rule of converting to base 10 for base conversion?

Converting between bases that are powers of two. Signup and view all the answers

When converting a number from Base x to Base y, which step is considered as the first in the conversion process?

Convert the number to base 10. Signup and view all the answers

If converting a number directly between two bases is sometimes possible, what should be considered first?

The relationship between the two bases. Signup and view all the answers

What type of bases might allow for faster conversions without using base 10 as an intermediary?

Bases that are powers of two. Signup and view all the answers

What is the first step in converting binary to octal?

Make groups of 3 bits from right to left for the integer part Signup and view all the answers

When completing an octet during conversion, where do you add zeros for the integer part?

On the left side Signup and view all the answers

What should you do with the digits after converting each octet to octal?

Concatenate the digits without any operations Signup and view all the answers

How are the bits grouped for the fractional part when converting from binary to octal?

From left to right Signup and view all the answers

If the binary number is 1011011.101, how should you group it for octal conversion?

10 110 11, 110 000 Signup and view all the answers