Converting binary numbers to floating point format using single-precision IEEE 754

In summary, the conversation was discussing how to convert the binary number 111011.0101 into floating point format using single-precision IEEE 754 format. The process involved identifying the negative sign, adjusting the exponent, and considering the role of the mantissa. The conversation also mentioned the need to consult the IEEE 754 standard for further guidance.
  • #1
brian.L
7
0

Homework Statement


The problem is how to begin converting 111011.0101 into floating point. I actually did begin looking at the first digit number "1" and identify that it is a negative since is one and zero is positive. Then I try working 111011.0101 separately by splitting 111011 for now and do 0101 after. I am not exactly sure if the decimal between the digits suggest a mantissa, so that is another question I need to be point out on.

Finally, believe I let the following digits 111011 represented by bits. For example: let first digit be 128, let second digit be 64, let third digit be 32, let forth digit be 16, etc.

Then I'm stuck on the part where calculation are suppose to be made?

Note: Here is the question in case I was not clear - Convert the following binary numbers to floating-point format using single-precision IEEE 754 format.
Convert your answer to hexadecimal format.


Convert this 111011.0101 to floating point.

Homework Equations


No equations. I'm not sure if there is suppose to be a mantissa somewhere in the digits.

The Attempt at a Solution


Unfinished solution, full calculations has not been completed yet.

Homework Statement

 
Last edited:
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  • #2


Help is appreciated :D
 
  • #3


brian.L said:

Homework Statement


The problem is how to begin converting 111011.0101 into floating point. I actually did begin looking at the first digit number "1" and identify that it is a negative since is one and zero is positive. Then I try working 111011.0101 separately by splitting 111011 for now and do 0101 after.
Since the most-significant bit is 1, the number is considered negative. The rest of the number's bit pattern is 11011.0101, with the first 1 removed.

Your number could be written in a quasi-scientific notation as -11011.0101 X 20. You can move the binary point to the left, simultaneously adjusting the exponent on 2. This is similar to changing 120.3 X 103 to 1.203 X 105.

So -11011.0101 X 20 = -.110110101 X 25.

You're going to have to look at IEEE 754 to see what else you need to do to convert this number to a floating point format.
brian.L said:
I am not exactly sure if the decimal between the digits suggest a mantissa, so that is another question I need to be point out on.

Finally, believe I let the following digits 111011 represented by bits. For example: let first digit be 128, let second digit be 64, let third digit be 32, let forth digit be 16, etc.

Then I'm stuck on the part where calculation are suppose to be made?

Note: Here is the question in case I was not clear - Convert the following binary numbers to floating-point format using single-precision IEEE 754 format.
Convert your answer to hexadecimal format.


Convert this 111011.0101 to floating point.

Homework Equations


No equations. I'm not sure if there is suppose to be a mantissa somewhere in the digits.

The Attempt at a Solution


Unfinished solution, full calculations has not been completed yet.
 
  • #4


Mark44 said:
Since the most-significant bit is 1, the number is considered negative. The rest of the number's bit pattern is 11011.0101, with the first 1 removed.

Your number could be written in a quasi-scientific notation as -11011.0101 X 20. You can move the binary point to the left, simultaneously adjusting the exponent on 2. This is similar to changing 120.3 X 103 to 1.203 X 105.

So -11011.0101 X 20 = -.110110101 X 25.

You're going to have to look at IEEE 754 to see what else you need to do to convert this number to a floating point format.

Oh, one more question. Is the question going to end up with a different result if there is mantissa?
 
  • #6


Mark44 said:
What do you think a mantissa is?

Mantissa replaces any first digit that are negative into zero?
 

What is the process for converting a binary number to single-precision IEEE 754 format?

The process involves separating the binary number into three parts: the sign bit, the exponent, and the mantissa. The sign bit determines whether the number is positive or negative. The exponent is used to shift the decimal point to the correct location, and the mantissa represents the significant digits of the number. These three parts are then combined to form the 32-bit binary representation in single-precision format.

What is the significance of the sign bit in single-precision IEEE 754 format?

The sign bit, located at the leftmost bit of the 32-bit representation, determines whether the number is positive or negative. A value of 0 indicates a positive number, while a value of 1 indicates a negative number.

How does the exponent affect the value of a number in single-precision IEEE 754 format?

The exponent is used to shift the decimal point to the correct location, allowing for a larger range of numbers to be represented in a compact 32-bit format. The exponent is also biased, meaning that a certain value is added to it before it is stored, in order to allow for both positive and negative exponents.

What is the mantissa in single-precision IEEE 754 format?

The mantissa represents the significant digits of the number. It is a fraction with a normalized value between 1 and 2, and is used in conjunction with the exponent to determine the final value of the number.

Are there any limitations or potential errors when converting to single-precision IEEE 754 format?

Yes, since the 32-bit format has a limited number of bits for the exponent and mantissa, there are limitations on the range and precision of numbers that can be represented. Additionally, there are some numbers that cannot be accurately represented in this format, leading to potential rounding errors.

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