(This article was first published on Statistic on aiR, and kindly contributed to R-bloggers)
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[1] <- x
q[i] <- xx[i] %/% 2
r[i] <- xx[i] %% 2
xx[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[1] <- x*2
nas[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)
[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 <- 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[1]==0) a <- a[-1]
else return(a)
}
}
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 <- 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[1] <- aa
q[i] <- xx[i] %/% 2
r[i] <- xx[i] %% 2
xx[i+1] <- q[i]
}
rr <- rev(r)
nas <- c()
nbs <- c()
xxs <- c()
for(i in 1:n)
{
xxs[1] <- bb*2
nas[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)
[1] "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) - 1
mantissa <- 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)
[1] "01000001001110100000000000000000"
dec.to.ieee754(11.33)
[1] "01000001001101010100011110101110"
You can verify the output with this Online Binary-Decimal Converter
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