PG1995
Full Member level 5
Hi
Most computers (I'm not sure if all) do most of the arithmetic using addition operation - i.e. subtraction, multiplication, and division all use addition operation. This makes circuit design simple and with only one circuit you get to do different things.
What I guess 1's and 2's complements let us do all operations, subtraction, division, and multiplication using addition method.
complement (noun)
2 c : a number that when added to another number of the same sign yields zero if the significant digit farthest to the left is discarded —used especially in assembly language programming
[M-W's Col. Dic.]
In base 10 the compliment of 3 would be 7 because 3+7 = 10 and after discarding the 1, we are left with 0
Thus 4 is the compliment of 6, and 8 of 2, etc.
The compliment of 55 would be 45, because 55+45=100 and removing the 1 leaves you with 0 again.
With binary, the compliment of 1 is 1 because 1+1 =10
The compliment of 1010 would be 0110 (which is 2's complement of 1010) because 1010 + 0110 = 10000 in binary.
1: Let's say we have a binary number 110 (6). It's 1's complement would be: 001 (1), and 2's complement would be: 010 (2). I don't see what 1's and 2's complements of the number tells us. Please help me with it.
2: Perhaps, using a particular example could help us a bit. We have binary number 1010 (10) and we want to subtract 110 (6) from it - i.e. 1010 - 110. In base 10 arithmetic it would be 10 - 6 = 4. So, how do complements help us here?
1's complement of 110 = 001 (1)
2's complement of 110 = 010 (2)
I do have more related queries on this topic but I would ask them after clearing this up. Thanks.
Scanned pages which can be useful:
1: **broken link removed**
2: https://img836.imageshack.us/img836/2465/floyddigitalfundamental.jpg
Most computers (I'm not sure if all) do most of the arithmetic using addition operation - i.e. subtraction, multiplication, and division all use addition operation. This makes circuit design simple and with only one circuit you get to do different things.
What I guess 1's and 2's complements let us do all operations, subtraction, division, and multiplication using addition method.
complement (noun)
2 c : a number that when added to another number of the same sign yields zero if the significant digit farthest to the left is discarded —used especially in assembly language programming
[M-W's Col. Dic.]
In base 10 the compliment of 3 would be 7 because 3+7 = 10 and after discarding the 1, we are left with 0
Thus 4 is the compliment of 6, and 8 of 2, etc.
The compliment of 55 would be 45, because 55+45=100 and removing the 1 leaves you with 0 again.
With binary, the compliment of 1 is 1 because 1+1 =10
The compliment of 1010 would be 0110 (which is 2's complement of 1010) because 1010 + 0110 = 10000 in binary.
1: Let's say we have a binary number 110 (6). It's 1's complement would be: 001 (1), and 2's complement would be: 010 (2). I don't see what 1's and 2's complements of the number tells us. Please help me with it.
2: Perhaps, using a particular example could help us a bit. We have binary number 1010 (10) and we want to subtract 110 (6) from it - i.e. 1010 - 110. In base 10 arithmetic it would be 10 - 6 = 4. So, how do complements help us here?
1's complement of 110 = 001 (1)
2's complement of 110 = 010 (2)
I do have more related queries on this topic but I would ask them after clearing this up. Thanks.
Scanned pages which can be useful:
1: **broken link removed**
2: https://img836.imageshack.us/img836/2465/floyddigitalfundamental.jpg