00001111 * 00000111 = ?

with explanation please?

Pick one as the multiplicand and the other as the multiplier. I'll pick 111 on the right as the multiplier, but it works either way.

Note that 111 = 1 + 10 + 100, so

1111*111 = 1111*(1 + 10 + 1100)

= 1111*1 + 1111*10 + 1111*100

= 1111 + 11110 + 111100

Add those in columns:

0 0 0 0 1 1 1 1

0 0 0 1 1 1 1 0

0 0 1 1 1 1 0 0

------------------

0 1 1 0 1 0 0 1

Check that in base ten. The product is 64+32+8+1 = 105, and 15*7 = 105 works in base ten too.

(Note that you have to carry 2 in some of those columns. Multiple bit carries occur with three or more addends in a sum. Add eleven or more numbers in a base ten column addition and you can get multiple-digit carries too.)

00001111 * 00000111 = ?

with explanation please?