CODEWITHSUNDEEP
mathfloating-pointieee-754
Kiimarii
Kiimarii

Reputation: 39

IEEE754 addition with one negative number

I have to add these two IEEE754 numbers:

-0,375 = 1 0111 1101 100 0000 0000 0000 0000 0000 // 
8,5 = 0 1000 0010 000 1000 0000 0000 0000 0000

I can add two positive numbers, but if one is negative I don't know how to do it! And i'm not allowed to subtract, it has to be an addition!!

Upvotes: 1

Views: 5052

Answers (1)

Dan Sp.
Dan Sp.

Reputation: 1447

Sign bit: 1 -> negative.

Exponent: 01111101 = 125 - 127 = -2 (Exponent is power of 2 of course).

Mantissa: 1000...... = 1.1 base 2 = 1.5

-1.5 x 2^(-2) = -0.375

Sign bit: 0 -> positive.

Exponent: 10000010 = 130 - 127 = 3.

Mantissa: 00010... = 1.0001 base 2 = 1.0625

1.0625 x 2^3 = 8.5

Line up exponents: I'll shift the -0.375 exponent by 5 to have the same exponent as the 8.5: -0.375 Mantissa only after shift: 0.000011

Next, I give both mantissas the same number of binary digits and precede them both with an extra zero. 01000100 and 00000011. The fact that they have 8 is coincidental. These are not bytes! Use as many digits as necessary from the mantissas.

Since the second one is supposed to be negative, take the 2's compliment: 11111101

Add:

01000100

11111101

101000001

Throw away extra leading bit when one is positive and one is negative: 01000001

Since the left most bit is 0 we have a positive number which should make sense. Strip it to leave the seven significant binary digits we started with after shifting for exponents: 1000001

Since the left bit is a one, we are good. We have 1.000001. Had you 'added' a bigger negative number, this left bit would become a zero and we would have to shift and change the exponent. But we do not. So......, It is positive (0), has exponent of 3 (10000010) we have:

0 1000 0010 000001000000........

Which happens to be 8.125

Upvotes: 2

Related Questions