binary question

[zwA4jE8b]

So I noticed that -122 in binary is 1000 0110 with leading 1's.

since 2^7 is 128 the h.o. nibble and the l.o. nibble is 6, does the computer just subtract 6 from 128 to get the 122?

[filipe]

Look for two's complement here: http://en.wikipedia.org/wiki/Signed_number_representations

[Disch]

Each bit has a weight of 2^n where n is the bit number

If the number is signed, the most significant bit has a negative weight

The value of the number is the sum of all bit weights, whose bit is set.

with 1000 0110, bits 1, 2, and 7 are set.

Therefore:

-(2^7) = -128  (negative because it is the most significant bit)
  2^2  =    4
  2^1  =    2
_____________
         -122

[moorecm]

since 2^7 is 128 the h.o. nibble and the l.o. nibble is 6, does the computer just subtract 6 from 128 to get the 122?

So basically, yes. Nice explanation, Disch.

[Disch]

Thanks.

The nibble doesn't really have anything to do with it though, since only the high bit is signed... not the high nibble.

[zwA4jE8b]

so 0101 is five but to sign it 1101 makes it -5 because the 1 is the most significant bit.

Thanks disch.

[zwA4jE8b]

or is it because when you negate 5 you get 1010 then add 1 making it 1101. so when the one is added are all bits except the h.o. bit shifted left? because it looks like adding 1 to 1010 would be 1011.

[Disch]

so 0101 is five but to sign it 1101 makes it -5 because the 1 is the most significant bit.

No

The most significant bit still has a weight of 2^n -- it's just that it's weight is negative.

So if you have a signed 4 bit number: 1101

that is bits 0, 2, 3. so:

2^3 = -8  (negative because it is signed, MSB)
2^2 =  4
2^0 =  1
________
    = -3

-5 would be 1011 (bits 0,1,3)

2^3 = -8
2^1 =  2
2^0 =  1
________
    = -5

EDIT:

because it looks like adding 1 to 1010 would be 1011.

Right. 1011 would be -5.

Inverting all bits, then adding 1 is a quick way to negate a number in 2's compliment.

[zwA4jE8b]

oh ok gotcha, I was looking at the chart on the wikipage link above and was looking in the wrong column when i got 1101 for -5..

Thank you, makes sense now.