How Does an Adder/Subtractor Unit Handle Negative Inputs?

[ECE]

If two 4 bit numbers are being added in the Adder/Subtractor unit e.g. X and Y. Then according to my textbook it is written that the Add/Sub Unit is built in a way that the add/sub signal (which chooses whether to add/subtract) is XOR with Y (the position where the number that is to be complemented is entered). But what if the user wants to enters { -5-3 }.How will the add/sub unit work then? Should the X input be also XOR with another signal similar to add/sub?

-Thanks

 

[rbj]

If two 4 bit numbers are being added in the Adder/Subtractor unit e.g. X and Y. Then according to my textbook it is written that the Add/Sub Unit is built in a way that the add/sub signal (which chooses whether to add/subtract) is XOR with Y (the position where the number that is to be complemented is entered).

but you must also add 1 to the inverted bits. you do that with this adder/subtractor by coupling in the same 1 that goes to the XORs (the add/subtract signal where add=0 and subtract=1) to the carry-in of the LSB (which is tied to 0 if you're adding).

But what if the user wants to enters { -5-3 }.How will the add/sub unit work then? Should the X input be also XOR with another signal similar to add/sub?

no, just put in for A the bit pattern for -5, which is the same bit pattern for an unsigned 4-bit number that is 16-5 or 11. so -5 is 1011 and you subtact 3 (0011) which gets complimented to 1100 and goes into your full-adder, but then you got to remember to couple in the 1 into the carry-in of the LSB (which effectively adds 1).

1011 + 1100 + 0001 = [1]1000

or -8 since the 1 that carries out falls off the edge.

 

[ravenprp]

Yes, in the case of adding or subtracting negative numbers, the X input should also be XORed with a signal similar to the add/sub signal. This is because when performing subtraction, the second number is typically converted to its 2's complement form, which involves flipping all the bits and adding 1. So if we want to add a negative number, we need to first convert it to its 2's complement form and then add it to the first number. This can be achieved by XORing the X input with a signal that indicates whether the number is positive or negative. This way, the add/sub unit can properly perform the addition or subtraction operation.