Convert 0.5937510 to a binary number, via octal.

Name: Problem 8, Chapter 5: Basic Engineering Mathematics
Uploaded: 2023-06-01T17:28:49-08:00
Duration: 7 min 5 s
Channel: Anas Venkitta
Description: Convert 0.5937510 to a binary number, via octal.

Key Concepts

Base Conversion Methods

These methods encompass the systematic approaches used to convert numbers between different bases. They include techniques such as repeated division for the integer part and repeated multiplication for the fractional part, ensuring that both components of the number are accurately transformed into the target numeral system.

Positional Numeral Systems

This concept involves the understanding that numbers in any numerical system are represented by digits whose values depend on their position and the base of the system. Recognizing how each position corresponds to a power of the base is essential when converting numbers between different numeral systems.

Fractional Conversion Techniques

Converting the fractional part of a number from one base to another typically involves multiplying the fraction by the target base, extracting the integer part, and iterating with the remaining fractional part. This method ensures that each digit in the new base is determined sequentially, which is crucial when dealing with non-integer values.

Intermediate Base Conversion

Using an intermediate base can simplify the conversion process, especially when the bases involved have a direct relationship. For example, converting via octal leverages the fact that each octal digit corresponds directly to a fixed number of binary digits, making the transition to binary straightforward.

Transcript

00:01 In the given question we are told that we should convert the decimal number that is the number with base 10 over here to a binary number via an octal number.

00:13 So, first we are told to convert this number into an octal number and then to a binary number ok.

00:20 So, to convert a decimal number which is of base 10 to an octal number, what we could do is we could see that in this specific case there are element this is a fractional number right.

00:36 So, there are elements to the right hand side of the decimal point and left hand side of the decimal point.

00:43 Since the element to the left hand side of the decimal point is 0, 0 is 0 in any base right in decimal base or the octal base 0 is still 0.

00:55 So, we are going to take when you convert this into a number which is of an octal base which is 8, you will still have 0 in the left hand side of the decimal point.

01:09 So, to find now to find what is in the right hand side over here in the octal number, what we do is we take this number 0 .59375 and multiply it with the base of an octal number which is 8 until we get only zeros towards the right hand side of this number.

01:33 So, this means we are going to multiply 0 .59375 with 8 and what we get over here is 4 .7500 right and now in the next step now we have multiplied this number once right once with 8.

01:53 So, now 4 is what we have got on the left hand side of the decimal number.

01:59 So, we can directly write 4 over here as the first number towards the right of the decimal point in the result that we are going to calculate.

02:10 In the next step, we are going to take again we are going to take the decimal value that is what is the value that is towards the right of the decimal point over here it is 0 .7500 and we are going to again multiply this with the number 8 and in this time what you get is you can see when you multiply 0 .75 with 8 what you get is 6 .0000.

02:43 So all the numbers towards the right has now become 0 and now the number that is in the right in the left hand side of the decimal point is 6 and this would be the next number that is in the resultant octal number.

03:03 So, now we have converted the decimal point decimal number into the octal number 0 .46.

03:12 So, the octal equivalent of the number 0 .59375 is 0 .46.

03:23 So, this is the first part of this question right...

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