# Convert decimal to IEEE-754 in R

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For some theory on the standard IEEE-754, you can read the Wikipedia page. Here I will post only the code of the function to make the conversion in R.

First we write some functions to convert decimal numbers to binary numbers:

decInt_to_8bit

For example, in 8-bit:

decInt_to_8bit(11, 8)

[1] 0 0 0 0 1 0 1 1

devDec_to_8bit(0.625, 8)

[1] 1 0 1 0 0 0 0 0

devDec_to_8bit(0.3, 8)

[1] 0 1 0 0 1 1 0 0

devDec_to_8bit(0.3, 16)

[1] 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0

We can delete the extra-zeros from the vectors, using these functions:

remove.zero.aft

So we have:

remove.zero.bef(decInt_to_8bit(11, 8))

[1] 1 0 1 1

```
```

`remove.zero.aft(devDec_to_8bit(0.625, 8))`

[1] 1 0 1

Binding these functions, we have:

dec.to.nbit

Example:

dec.to.nbit(11.625,8)

[1] "1011.101"

Now we can write the code for the decimal to IEEE-754 single float conversion in R:

dec.to.ieee754

The numbers 11.625 and 11.33 in IEEE-754 are:

dec.to.ieee754(11.625)

[1] "01000001001110100000000000000000"

```
```

`dec.to.ieee754(11.33)`

[1] "01000001001101010100011110101110"

You can verify the output with this Online Binary-Decimal Converter

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