gtools (version 3.9.5)

baseOf: Transform an integer to an array of base-n digits

Description

Transform an integer to an array of base-n digits

Usage

baseOf(v, base = 10, len = 1)

Arguments

v

A single integer value to be transformed.

base

The base to which to transform to.

len

The minimal length of the returned array.

Author

Steffen Moeller

Details

This function converts the elements of an integer vector as an array of its digits. The base of the numbering scheme may be changed away from 10, which defines our decimal system, to any other integer value. For base=2, the number is returned in the binary system. The least significant digit has the highest index in the array, i.e. it appears on the right. The highest exponent is at position 1, i.e. left.

To write decimal values in another base is very common in computer science. In particular at the basis 2 the then possible values 0 and 1 are often interpreted as logical false or true. And at the very interface to electrical engineering, it is indicated as an absence or presence of voltage. When several bit values are transported synchronously, then it is common to give every lane of such a data bus a unique 2^x value and interpret it as a number in the binary system. To distinguish 256 characters one once needed 8 bit ("byte"). It is the common unit in which larger non-printable data is presented. Because of the many non-printable characters and the difficulty for most humans to memorize an even longer alphabet, it is presented as two half bytes ("nibble") of 4 bit in a hexadecimal presentation. Example code is shown below.

For statisticians, it is more likely to use bit representations for hashing. A bit set to 1 (TRUE) at e.g. position 2, 9 or 17 is interpreted as the presence of a particular feature combination of a sample. With baseOf, you can refer to the bit combination as a number, which is more easily and more efficiently dealt with than with an array of binary values. The example code presents a counter of combinations of features which may be interpreted as a Venn diagram.

Examples

# decimal representation
baseOf(123)

# binary representation
baseOf(123, base = 2)

# octal representation
baseOf(123, base = 8)

# hexadecimal representation
baseOf(123, base = 16)

# hexadecimal with more typical letter-notation
c(0:9, LETTERS)[baseOf(123, 16)]

# hexadecimal again, now showing a single string
paste(c(0:9, LETTERS)[baseOf(123, 16)], collapse = "")

# decimal representation but filling leading zeroes
baseOf(123, len = 5)

# and converting that back
sum(2^(4:0) * baseOf(123, len = 5))

# hashing and a tabular venn diagram derived from it
m <- matrix(sample(c(FALSE, TRUE), replace = TRUE, size = 300), ncol = 4)
colnames(m) <- c("strong", "colorful", "nice", "humorous")
names(dimnames(m)) <- c("samples", "features")
head(m)

m.val <- apply(m, 1, function(X) {
  return(sum(2^((ncol(m) - 1):0) * X))
})
m.val.rle <- rle(sort(m.val))
m.counts <- cbind(
  baseOf(m.val.rle$value, base = 2, len = ncol(m)),
  m.val.rle$lengths
)
colnames(m.counts) <- c(colnames(m), "num")
rownames(m.counts) <- apply(m.counts[, 1:ncol(m)], 1, paste, collapse = "")
m.counts[1 == m.counts[, "nice"] & 1 == m.counts[, "humorous"], , drop = FALSE]
m.counts[, "num", drop = TRUE]