358 in binary single floating point using excess 4

In summary, to express 358 in binary single floating point format using excess 4 notation, the value would be represented as 0100000101100110, with the sign being 0, the exponent being 100 (or 0 in excess-4), and the mantissa being 000101100110 (assuming the first 1 is implied). This format follows the standard representation with a 1-bit sign, 3-bit exponent, and 28-bit mantissa. The value 328 can be represented within the given 28 bits, so there is no need to move the decimal point, resulting in an exponent of 0 in excess-4.
  • #1
francisg3
32
0
i need to express 358 in binary single floating point format using excess 4 notation...i can do it easily using the 32-bit standard representation with the excess 127 exponent. i know that 358 is 101100110 therefore i assume floating point would be 1.01100110 with an exponent of 8. i know excess 4 is the base exponent added to 4 but 8+4=12 which cannot be represented with 4 bits. any help would be greatly appreciated! thanks.
 
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  • #2
12 can be represented in 4 bits:

1100 = 0*20 + 0*21 + 1*22 + 1*23 = 12
 
  • #3
I would guess this would mean that you have 1 bit for the sign, 3 bits for the exponent (3 bits to represent the values from -4 to +3 in excess-4), and the remaining 28 bits for the mantissa.

The value 328 can be represented within the given 28 bits, so there is no need to move the decimal point, therefore the exponent is 0 (which equates to 100 in excess-4).

So, 328 should be represented as:
0 100 0000 0000 0000 0000 0001 0110 0110
or 40000166 hex
 
  • #4
well the answer is supposed to be in this format:
SEEEMMMMMMMMMMMM
the answer is supposed to be in normalized format. The sign is easy (i know it's 0) it's the rest I'm having trouble with. I can do excess-127 notation with no problem, it's the excess-4 business I'm not catching.
 
  • #5
francisg3 said:
well the answer is supposed to be in this format:
SEEEMMMMMMMMMMMM
the answer is supposed to be in normalized format. The sign is easy (i know it's 0) it's the rest I'm having trouble with. I can do excess-127 notation with no problem, it's the excess-4 business I'm not catching.

Easy enough then (you didn't state that it was to be 16-bit, so I assumed 32-bit)

The value would then be:
0100000101100110

the sign is 0
the exponent is 100 (or 0 in excess-4)
the mantissa is 000101100110
 

1. What is "358 in binary single floating point using excess 4"?

"358 in binary single floating point using excess 4" refers to a way of representing the number 358 in binary form using a single precision floating point format with an excess 4 bias. This is a common method used in computer systems to store and manipulate numbers with decimal values.

2. How is "358 in binary single floating point using excess 4" calculated?

The calculation for "358 in binary single floating point using excess 4" involves converting the integer part of the number to binary and then adding the excess 4 bias to the exponent. The fractional part of the number is then represented in binary using the remaining bits. The resulting binary representation is then normalized to the proper format for single precision floating point numbers.

3. What is the purpose of using excess 4 in "358 in binary single floating point using excess 4"?

The purpose of using excess 4 in "358 in binary single floating point using excess 4" is to allow for both positive and negative numbers to be represented in a simpler way. By adding a bias, the range of numbers that can be represented is increased, making it easier to perform mathematical operations on these numbers.

4. How accurate is "358 in binary single floating point using excess 4"?

The accuracy of "358 in binary single floating point using excess 4" depends on the precision of the floating point format being used. In this case, single precision floating point numbers have a precision of approximately 7 decimal digits. This means that the binary representation of "358 in binary single floating point using excess 4" is accurate to 7 decimal places.

5. What are the advantages of using "358 in binary single floating point using excess 4" over other forms of representation?

One advantage of using "358 in binary single floating point using excess 4" is that it allows for a wider range of numbers to be represented compared to other forms of representation, such as fixed point or integer representation. It also makes it easier to perform mathematical operations on these numbers. Additionally, the use of excess 4 allows for both positive and negative numbers to be represented in a simpler way.

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