Good evening. I am a computer science major and new to all the programming and such. I am having problems with some of my homework.

I have to add these numbers using twos complement.

1010+1101=
0100+1011=
1010+0100=
1101+1011=

I dunno if i am doing this right but I get


1010+1101=0101+0010=0101
0100+1011=1011+0100=1111
1010+0100=0101+1011=1 1000
1101+1011=0010+0100=0110

Are these correct? How would I go adding these numbers using twos complement. I also habe another homework problem that is kinda stressing me out and I do not know how to go solving it.

Assuming common Intel (i386) float representation, 32 bits (sign 1 bit, exponent 8 bits, mantissa 2 bits)

What is the largest positive number you can represent?
what is the smallest non-zero number you can represent?
what is the smallest negative non zero number you can represent?



Any help would be GREATLY appreciated.

Are you assuming four-bit binary numbers that represent 2's complement signed integers?

Then the values are:
The big advantage of 2's complement representation of signed integers is that addition follows the rules of 'straight' binary addition. If there was no overflow, you will the the "right" answer.

If I just add the first two using binary arithmetic:
If I'm only supposed to use 4-bit arithmetic then the result is 0111 binary.

If I convert the numbers to decimal and add them I get

Note that -9 decimal is not representable in our 4-bit 2's complement number system. What happened? It's called overflow. Looking back at the binary results, we see that we added two negative numbers and got a positive number. (That's probably bad, right?)

Note that if I add a negative number and a positive number, there can't possibly be an overflow, right?

But adding two positive numbers may (or may not) result in an overflow, as is in the case of adding two negative numbers.


Don't you have a book? Aren't there any explanations/examples?

Just do "straight" binary addition: Start with least significant bits. Add the bits according to the definition of binary addition and then move up the line. At each bit you add in the carry from the next less significant bit addition.

Huh? Why don't they add up to 32 bits? Intel didn't invent floating point, you know. Maybe the assignment is referring to IEEE 754

It is the (positive) number with the largest possible exponent value and the largest possible mantissa value, right? Then, according to the rules that you must have been given for evaluating floating point numbers, what is the decimal value?
Do you mean the negative number closest to zero (the negative number with smallest absolute value), or the most negative number that can be represented?


Regards,

Dave