Simple Maths questions? and binary addition/subtraction?

[fouadalnoor]

Hello guys,

I know this is really silly but I am a little confused about how to do the following operation by hand:

0.25-0.5? or any similar questions

Also, when it comes to fixed point signed numbers, how do you subtract them?

Say I choose my MSB to be the sign and the 7th bit in an 8 bit number to be 1, while bits 6-0 are the fractional part as shown below:

[SIGN][2^0][2^-1][2^-2][2^-3][2^-4][2^-5][2^-6]

So for example: 01.100000 is 1.5 in decimal.

When aligning the decimal point its easy to add say 1+0.25:

01.000000
+00.010000
=01.010000 = 1.25 in decimal

But how would I do 1-0.25?

Hope you can help!

 

[Mike odom]

01000000
-00010000
=
00110000 = 0.5 + 0.25 = 0.75
rules:
1-0 = 1
1-1=0
0-1 = 1 with a borrow (all zeros upstream become 1 until first 1 hit which becomes 0), if there are no ones upstream, the overflow flag is set (overflow/borrow).

 

[fouadalnoor]

01000000
-00010000
=
00110000 = 0.5 + 0.25 = 0.75
rules:
1-0 = 1
1-1=0
0-1 = 1 with a borrow (all zeros upstream become 1 until first 1 hit which becomes 0), if there are no ones upstream, the overflow flag is set (overflow/borrow).

Ah, thanks! Its the 0-1 that is confusing me... but if I had to do 0.25-1 then wouldnt that be: 11010000? but that is not -0.75, it gives me -1.25? is that because there is overflow?

 

[Mike odom]

with the sign bit as bit 7, you don't use a '1' for the bit, you use a zero, so a -1 would look like 10111111,
so .25 plus - 1 would look like:

00010000
10111111
and adding them, you'd get:
11001111
which is -.75

for instance, if you don't imply the decimal, a 1 looks like 00000001, a zero 00000000, and minus one 11111111 (the next one below zero), and minus two 11111110, minus three 11111101, etc... it's called sign bit extension for negative numbers

 

[Jaguarjoe]

No sweat, just convert to Roman numerals first