Discrete Mathematics

---------------------------SYMBOLIC

LOGIC

57

In doing this we see a general pattern. Suppose we are in a particular column and are repeating the

pattern

of

n Ts, followed by n Fs.

If

we move one column left, we double the number

of

Ts followed by double

the number

of

Fs; that is, 2n Ts, followed by 2n Fs.

Why does this work? Well, it is related to the previous section. Think

ofT

as being I and F as being 0.

Look at row

I.

There are three

t's

in this row. Convert it to a binary number. This will be

Ill.

Now, we go to

row 2. Reading across, we read T, T, F. Converting

to

Is

and

Os,

we get 110.

In

binary, this is 6. Now, as we

progress down from ...