how to subtract binary number?

Question

can anyone show me the mthod of subtract in detail?

Answer 1

Just like base 10, except only zeroes and ones:

Example:

1100
- 111
-------
Last colomn:
0 - 1 (borrow) becomes 10-1 =1

2nd-last column:
Now 0 - 1 becomes 10 - 1, but since you already "borrowed",
it's now 1 -1 = 0

Now we're left with 11 - 1, but again we've borrowed, so it's 10 - 1 = 1

Solution: 101

Now check it by adding:

111 + 101 and see.

Answer 2

Consider the example 8 - 6 = 2 in binary
use the result that 10 - 1 = 1
8----4----2-----1
1----0----0-----0
------1---1------0
The units column is 0 = 0 (no problem there!)
The next operation is to subtract 1 two from 0 twos which can`t be done so have to take the 1 from the 8 column and put a 1 into 4 column and a 10 into the 2 column. Note that 10 in the two column is the same as 1 in 4 column.

Lay out then becomes:-
8-----4-------2-------1
0-----1-------10------0
0-----1-------1-------0
0-----0-------1-------0
Answer is 10 in base two = 2 in base ten
Check 8 - 6 = 2
Another method is to convert to base ten and then convert back again.
Example 2
1000 - 110 = 8 - 6 = 2 in base ten = 10 in base two.

Answer 3

Lets try 2 - 1

10
01
---------

we need to use the principle of borrowing.

0 - 1 = 1 with a borrow

10
01
----
..1

Now the next column we have 1 - 0 but there is a borrow so there is a zero here.

10
01
----
01

If you look into two's complement you can learn the modern way that computer hardware does arithmetic.