Question about four bit decrementor

The question along with solution is attached
Can anybody explain me solution. This is from book of Mooris Mano

Hi,

Are you familiar with two's compliment arithmetic? This arithmetic allows us to perform subtractions by doing additions.

In algebra, decrementing by one is the same as adding the opposite:
decrement-by-one = n-1 = n +-1

So, we can use adders to perform subtraction.

We can represent minus 1 by it's two's compliment form:
- 0001 >>> 1110 + 1 >>> 1111

Now we can add 1111 to the original number to do the decrement:

Lets try decrement 12:
12 >> C >> 1100
1100 - 1
1100 - 0001
1100 + 1111 (using twos compliment)
1100 (12d)
1111 (-1d)
+------
(1)1011 (11d)

Note: in true signed arithmetic the msb represents the sign. In this problem we should extend the nibble to 5 bits and then we will see a positive result...
01100 (12d)
11111 (-1d)
+------
01011 (+11d)

jpvSoccer is correct. flip the bits and then increment by one!

Yes i understand all of 2's complement but kindly explain me the figure
He is adding one to each full adder, that is Ok, where he is taking 1's comoplement???

Hi, sorry for the confusion.

He is adding 1111 (-1d) not just 1 to each adder. 1111 is the two's complement of -1d.

Does this help?

jpvSoccer said:

Hi, sorry for the confusion.

He is adding 1111 (-1d) not just 1 to each adder. 1111 is the two's complement of -1d.

Does this help?

Click to expand...

Thanks a lot .
u people are really like a beacon for this forum

You can verify it yourself by simulating it online:**broken link removed**. Just use full-adder elements under Arith.