/** Converts a string of digits in the base, possibly containing a decimal point, to a JS number */
function digitsToNumber(numStr, base = 2) {
const numberOfDecimalDigits = (numStr.split(".")[1] || "").length;
const digitsWithoutDecimalPoint = numStr.replace(".", "");
return (
parseInt(digitsWithoutDecimalPoint, base) / Math.pow(base, numberOfDecimalDigits)
);
}
digitsToNumber("10.1", 2)
digitsToNumber("10.1", 2).toString(2)
vlembed(makeTreeVegaSpec(binaryTreeNodes))
aBinaryTree = {
const rootNode = new BinaryTreeNode(null, "0");
const zero = new BinaryTreeNode(rootNode, "0");
const oneHalf = new BinaryTreeNode(rootNode, "1"); // == 0.1
const alsoZero = new BinaryTreeNode(zero, "0"); // == 0.00
const alsoOneHalf = new BinaryTreeNode(oneHalf, "0"); // == 0.10
const oneQuarter = new BinaryTreeNode(zero, "1"); // == 0.01
const threeQuarters = new BinaryTreeNode(oneHalf, "1"); // == 0.11
return rootNode;
}
binaryTreeNodes = aBinaryTree.traverseTree()
// Class used only to create (or find) the number 0.
// To create other rational numbers with an infinite trailing '0's, use Rational.construct.
class Zero extends Rational {
static construct(digitsNode, index = 0, name = "Zero") {
const newReal = super.construct(digitsNode, index, name, [], ["0"]);
return newReal;
}
}
class One extends Rational {
static construct(digitsNode, index = 0, name = "One") {
const newReal = super.construct(digitsNode, index, name, [], ["1"]);
return newReal;
}
}
function simpleExampleNumberGenerator() {
// The following construction of the rootNode and numbers Zero and One is
// copied to each of the generator functions, with small variations.
// Enumeration of all numbers.
const numbers = [];
let index = 0;
// Generate root of tree, 0.
const rootNode = new BinaryTreeNode(null, "0");
// Generate numbers for 0 and 1, the infinite strings of all '0's and all '1's.
const zero = Zero.construct(rootNode.addDigit("0"), index++, "Zero"); // 0.00̅
const one = One.construct(rootNode.addDigit("1"), index++, "One"); // 0.11̅
// Append to numbers array.
numbers.push(zero);
numbers.push(one);
// Add one more digit to zero and one.
zero.addNextDigit(); // == "0.000̅"
one.addNextDigit(); // == "0.111̅"
// Add '1' digit to zero.node.parent, and create a number for 0.01...
const node01 = zero.node.parent.addDigit("1");
const zeroone = Real.construct(
node01,
index++,
'A number starting with "0.01"'
);
numbers.push(zeroone);
// Add '0' digit to one.node.parent, and create a number for 0.10...
const node10 = one.node.parent.addDigit("0");
const onezero = Real.construct(
node10,
index++,
'A number starting with "0.10"'
);
numbers.push(onezero);
// Return list of nodes by traversing the binary tree.
return { numbers, tree: rootNode.traverseTree() };
}
vlembed(makeTreeVegaSpec(simpleExampleNumbers.tree))
showEnumerationTable(simpleExampleNumbers)
showEnumerationTable(ratiosOfOneDenominator)
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