The attached file gives functions to go both directions. I have used
it in class for many years.
This is very useful when studying machine representations of numbers,
for understanding mixed-radix number systems, for example time (days, hours,
minutes, seconds) or British money (pounds, shillings, pence), and for unique
indexing of cells in designed experiments.
Rich
## base
## Richard M. Heiberger
## See Section 12.1.4.2 of
## Richard M. Heiberger
## Computation for the Analysis of Designed Experiments
## Wiley, 1989
## defaults to 8 bit binary
base <- function(x, basis=c(2,2,2,2,2,2,2,2)) {
cb <- rev(cumprod(c(1,basis)))
xx <- x
y <- rep(0, length(cb))
for (i in 1:length(cb)) {
yy <- xx %/% cb[i]
if (yy > 0) {
y[i] <- yy
xx <- xx %% cb[i]
}
}
names(y) <- cb
y
}
baseinv <- function(y, basis=c(2,2,2,2,2,2,2,2)) {
sum(y * rev(cumprod(c(1,basis))))
}
base(200)
baseinv(.Last.value)
## British money
basis <- c(12,20) ## 12 pence per shilling, 20 shillings per pound sterling
base(498, basis)
baseinv(.Last.value, basis)
## American weight
base(100, 16) ## 16 ounces per pound avoirdupois
baseinv(.Last.value, 16)
## time
basis <- c(60,60,24) ## 60 seconds per minute, 60 minutes per hour, 24 hours
per day
x <- c(1, 2, 3, 40)
y <- baseinv(x, basis)
y
base(y, basis)
## binary arithmetic with 8 bits
basis <- c(2,2,2,2,2,2,2,2)
x <- 100
y <- base(x, basis)
y
baseinv(y, basis)
base(1)
baseinv(.Last.value)
base(200)
baseinv(.Last.value)
base(1000)
baseinv(.Last.value)
## IEEE with 53 base 2 digits
x <- c( 100000000000001, 100000000000002, 100000000000003,
1000000000000001, 1000000000000002, 1000000000000003,
10000000000000001, 10000000000000002, 10000000000000003 ## the last
three values illustrate
) ## the effects
of .Machine$double.eps
x
sprintf("%17.0f", x)
y <- sapply(x, base, basis=rep(2,54))
y
print(digits=17,
apply(y, 2, baseinv, basis=rep(2,54))
)
## base 9
a <- base(132, c(9,9,9))
b <- base(125, c(9,9,9))
a
b
a+b
baseinv(a+b, c(9,9,9))
base(baseinv(a+b, c(9,9,9)), c(9,9,9))
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