How can I generate the opposite color according to current color?

UPDATE: Production-ready code on GitHub.

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This is how I’d do it:

1. Convert HEX to RGB
2. Invert the R,G and B components
3. Convert each component back to HEX
4. Pad each component with zeros and output.

function invertColor(hex) {
    if (hex.indexOf('#') === 0) {
        hex = hex.slice(1);
    }
    // convert 3-digit hex to 6-digits.
    if (hex.length === 3) {
        hex = hex[0] + hex[0] + hex[1] + hex[1] + hex[2] + hex[2];
    }
    if (hex.length !== 6) {
        throw new Error('Invalid HEX color.');
    }
    // invert color components
    var r = (255 - parseInt(hex.slice(0, 2), 16)).toString(16),
        g = (255 - parseInt(hex.slice(2, 4), 16)).toString(16),
        b = (255 - parseInt(hex.slice(4, 6), 16)).toString(16);
    // pad each with zeros and return
    return '#' + padZero(r) + padZero(g) + padZero(b);
}

function padZero(str, len) {
    len = len || 2;
    var zeros = new Array(len).join('0');
    return (zeros + str).slice(-len);
}

Example Output:

Advanced Version:

This has a bw option that will decide whether to invert to black or white; so you’ll get more contrast which is generally better for the human eye.

function invertColor(hex, bw) {
    if (hex.indexOf('#') === 0) {
        hex = hex.slice(1);
    }
    // convert 3-digit hex to 6-digits.
    if (hex.length === 3) {
        hex = hex[0] + hex[0] + hex[1] + hex[1] + hex[2] + hex[2];
    }
    if (hex.length !== 6) {
        throw new Error('Invalid HEX color.');
    }
    var r = parseInt(hex.slice(0, 2), 16),
        g = parseInt(hex.slice(2, 4), 16),
        b = parseInt(hex.slice(4, 6), 16);
    if (bw) {
        // https://stackoverflow.com/a/3943023/112731
        return (r * 0.299 + g * 0.587 + b * 0.114) > 186
            ? '#000000'
            : '#FFFFFF';
    }
    // invert color components
    r = (255 - r).toString(16);
    g = (255 - g).toString(16);
    b = (255 - b).toString(16);
    // pad each with zeros and return
    return "#" + padZero(r) + padZero(g) + padZero(b);
}

Example Output: