Page 371 - Analog and Digital Filter Design

368 Analog and Digital Filter Design

one equals two. This is a bit corny but “one’s-complement, plus one, equals
two’s-complement. ”

Binary Number 01 1 1,011 1,0001,1010 (771Ah)
One’s Complement 1000,1000,1110,0101 (88E5h)
+1 0000,0000,0000,000 1

Two’s Complement 1000,1000,1110,0110 (88E6h)

The two’s complement number 88E6h is therefore the negative signed equiva-
lent of 771Ah.

We can transform a hexadecimal number directly into a number with the same
magnitude but with a negative sign. This can be done without having to convert
it into binary first. Transformation is done by subtracting the hexadecimal
number from FFFFh and then adding one:

FFFF
Subtract Number 771A
Result 88E5

Add 000 1 h 88E6

The result is a number with a magnitude equal to 771Ah but with a negative
sign. Alternatively, subtract the hexadecimal number from 1,0000h, or 2” where
n is the number of bits in the original number. In this case = 4.

Strangely, these techniques also work when going from a negative number to
find its positive magnitude. Logic indicates that a lh should be subtracted
instead of added in this case. However, by using the same numbers, it can be
easily shown that an addition of lh is still required. The inversion process works
whether the number being inverted is positive or negative. The technique should
perhaps be thought of as a sign-changing process.

FFFF
Subtract Number 88E6

Result 7719
Add 000 1 h 771A

The result is the magnitude of the negative number. I will be using this tech-
nique in examples given later.