Need solution for combinations of bits according to checkboxes

To prevent you from asking basic questions like this, you would be best served by learning to do math in binary and hexadecimal.

I'm dead serious on this. Google "Binary math" and "bitwise operators" and start reading. You can't go through life writing code without knowing this stuff.

I'm going to assume that in addition to setting the 'Checked property of the CheckBoxes based on a byte value ... as Karthik neatly shows you how to do, that you also want to read the CheckBoxes' checked state, and construct a byte value.

// declare a list of CheckBoxes
private List<checkbox> cbList = new List<checkbox>(); 

// somewhere in code, perhaps in a Form Load Event initialize the List
cbList.AddRange(new CheckBox[]
{
  checkBox1, checkBox2, checkBox3, checkBox4, checkBox5, checkBox6, checkBox7, checkBox8
});

// function to read the CheckBoxes and return a byte value
private byte getByteFromCheckBoxes()
{
    byte b = 0x0;

    for (int i = 0; i < 8; i++)
    {
        if(cbList[i].Checked) b += Convert.ToByte(Math.Pow(2, i));
    }

    return b;
}

// test the function at run-time
private void button1_Click(object sender, EventArgs e)
{
    byte checkByte = getByteFromCheckBoxes();
}

For eliminating the computation in the function above ... which I'd want to do if generating a byte from the CheckBoxes was occurring frequently ... I'd consider using a Dictionary:

private Dictionary<CheckBox, byte> dctChkByte;

// initialize somewhere in code
dctChkByte = new Dictionary<checkbox,>
{
    {checkBox1, 0x01},
    {checkBox2, 0x02},
    {checkBox3, 0x04},
    {checkBox4, 0x08},
    {checkBox5, 0x10},
    {checkBox6, 0x20},
    {checkBox7, 0x40},
    {checkBox8, 0x80},
};

// use in a function
private byte getByteFromCheckBoxes2()
{
    byte b2 = 0x0;

    foreach (CheckBox theCheckBox in dctChkByte.Keys)
    {
        if (theCheckBox.Checked) b2 += dctChkByte[theCheckBox];

        // note that you cannot do this: write Microsoft
        // and complain if this makes you unhappy !
        // b2 += (theCheckBox.Checked) ? dctChkByte[theCheckBox] : 0x0;
    }

    return b2;
}