# Convert decimal to IEEE-754 in R

October 6, 2010
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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 <- function(x, precs) {q <- c()r <- c()xx <- c()for(i in 1:precs){xx <- xq[i] <- xx[i] %/% 2r[i] <- xx[i] %% 2xx[i+1] <- q[i]}rr <- rev(r)return(rr)}`

``` ```

`devDec_to_8bit <- function(x, precs) {nas <- c()nbs <- c()xxs <- c()for(i in 1:precs){xxs <- x*2nas[i] <- (xxs[i]) - floor(xxs[i])nbs[i] <- trunc(xxs[i], 1)xxs[i+1] <- nas[i]*2}return(nbs)}`

For example, in 8-bit:

`decInt_to_8bit(11, 8) 0 0 0 0 1 0 1 1`

`devDec_to_8bit(0.625, 8) 1 0 1 0 0 0 0 0`

`devDec_to_8bit(0.3, 8) 0 1 0 0 1 1 0 0devDec_to_8bit(0.3, 16) 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 <- function(a) {n <- length(a)for(i in n:1){if (a[n]==0) a <- a[-n]else return(a)n <- n-1}}`

``` ```

`remove.zero.bef <- function(a) {n <- length(a)for(i in 1:n){if (a==0) a <- a[-1]else return(a)}}`

So we have:

`remove.zero.bef(decInt_to_8bit(11, 8)) 1 0 1 1`

``` ```

`remove.zero.aft(devDec_to_8bit(0.625, 8)) 1 0 1`

Binding these functions, we have:

```dec.to.nbit <- function(x,n) {aa <- abs(trunc(x, 1))bb <- abs(x) - abs(trunc(x)) q <- c()r <- c()xx <- c()for(i in 1:n){xx <- aaq[i] <- xx[i] %/% 2r[i] <- xx[i] %% 2xx[i+1] <- q[i]}rr <- rev(r) nas <- c()nbs <- c()xxs <- c()for(i in 1:n){xxs <- bb*2nas[i] <- (xxs[i]) - floor(xxs[i])nbs[i] <- trunc(xxs[i], 1)xxs[i+1] <- nas[i]*2}```

``` ```

`bef <- paste(remove.zero.bef(rr), collapse="")aft <- paste(remove.zero.aft(nbs), collapse="")bef.aft <- c(bef, aft)strings <- paste(bef.aft, collapse=".")return(strings)}`

Example:

`dec.to.nbit(11.625,8) "1011.101"`

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

```dec.to.ieee754 <- function(x) {aa <- abs(trunc(x, 1))bb <- abs(x) - abs(trunc(x)) rr <- decInt_to_8bit(aa, 32) ppc <- 24 - length(remove.zero.bef(rr)) nbs <- devDec_to_8bit(bb, ppc) bef <- remove.zero.bef(rr)aft <- remove.zero.aft(nbs) exp <- length(bef) - 1mantissa <- c(bef[-1], aft) exp.bin <- decInt_to_8bit(exp + 127, 16)exp.bin <- remove.zero.bef(exp.bin) first <- c()if (sign(x)==1) first=c(0)if (sign(x)==-1) first=c(1)```

``` ```

```ieee754 <- c(first, exp.bin, mantissa, rep(0, 23-length(mantissa)))ieee754 <- paste(ieee754, collapse="") return(ieee754)}```

The numbers 11.625 and 11.33 in IEEE-754 are:

`dec.to.ieee754(11.625) "01000001001110100000000000000000"`

``` ```

`dec.to.ieee754(11.33) "01000001001101010100011110101110"`

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

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