Two's complement notation

The most popular system for representing integers within today’s computers is
two’s complement notation. This system uses a fixed number of bits to represent each of the values in the system. In today’s equipment, it is common to use
a two’s complement system in which each value is represented by a pattern of
32 bits. Such a large system allows a wide range of numbers to be represented
but is awkward for demonstration purposes. Thus, to study the properties of two’s
complement systems, we will concentrate on smaller systems.
Figure 1.19 shows two complete two’s complement systems—one based on
bit patterns of length three, the other based on bit patterns of length four. Such
a system is constructed by starting with a string of 0s of the appropriate length
and then counting in binary until the pattern consisting of a single 0 followed by
1s is reached. These patterns represent the values 0, 1, 2, 3, . . . . The patterns
representing negative values are obtained by starting with a string of 1s of the
appropriate length and then counting backward in binary until the pattern consisting of a single 1 followed by 0s is reached. These patterns represent the values
-1, -2, -3, . . . . (If counting backward in binary is difficult for you, merely start
at the very bottom of the table with the pattern consisting of a single 1 followed
by 0s, and count up to the pattern consisting of all 1s.)
Note that in a two’s complement system, the leftmost bit of a bit pattern indicates the sign of the value represented. Thus, the leftmost bit is often called the
sign bit. In a two’s complement system, negative values are represented by the
patterns whose sign bits are 1; nonnegative values are represented by patterns
whose sign bits are 0.
In a two’s complement system, there is a convenient relationship between the
patterns representing positive and negative values of the same magnitude. They
are identical when read from right to left, up to and including the first 1. From
there on, the patterns are complements of one another. (The complement of a
pattern is the pattern obtained by changing all the 0s to 1s and all the 1s to 0s;
0110 and 1001 are complements.) For example, in the 4-bit system in Figure 1.19 the patterns representing 2 and -2 both end with 10, but the pattern representing 2 begins with 00, whereas the pattern representing -2 begins with 11.
This observation leads to an algorithm for converting back and forth between bit
patterns representing positive and negative values of the same magnitude. We
merely copy the original pattern from right to left until a 1 has been copied, then
we complement the remaining bits as they are transferred to the final bit pattern
(Figure 1.20).
Understanding these basic properties of two’s complement systems also leads
to an algorithm for decoding two’s complement representations. If the pattern to be decoded has a sign bit of 0, we need merely read the value as though the
pattern were a binary representation. For example, 0110 represents the value 6,
because 110 is binary for 6. If the pattern to be decoded has a sign bit of 1, we
know the value represented is negative, and all that remains is to find the magnitude of the value. We do this by applying the “copy and complement” procedure in Figure 1.20 and then decoding the pattern obtained as though it were a
straightforward binary representation. For example, to decode the pattern 1010,
we first recognize that since the sign bit is 1, the value represented is negative.
Hence, we apply the “copy and complement” procedure to obtain the pattern
0110, recognize that this is the binary representation for 6, and conclude that the
original pattern represents -6.

Tror uttrycken som används vid programmering är signed/unsigned (numbers/integers).

Två kompliment i binärbas är representationen av ett binärt tal där den största värdesiffran just visar om det är ett negativt eller positivt tal.

Du tänker rätt i att texten är (onödigt) komplex.

För att svara på din fråga, "two complement notation" är inget magiskt integertal eller nummertyp. Du kan läsa samma tal som om det vore en "unsigned" men då blir ju syftet/värdet med siffran troligen helt fel. Inte helt ovanligt fel att göra. Kort och gott är det inget speciellt med "1001", det handlar bara om perspektiv och om man anser att det är ett "signed/unsigned" tal.

Signed (1001) = -7
Unsigned (1001) = 9

För dataingenjören som jobbar på lågnivå så är det rätt arbiträrt om det binära tvåkomponent-talet är negativt/positivt och det är lite charmen med det hela när man ska jobba med talen i hårdvara. (Visst, lite handpåläggning krävs såklart)

signed/unsigned är väl generella uttryck inom programmering som funnits åtminstone så länge det funnits datorer, och troligtvis längre än så. "sign" syftar ju på vilket tecken talet har framför sig, + eller -, och använder man binär representation så måste man också ha något sätt att representera tecknet där tvåkomplement är det vanligaste idag.

Jag vet för övrigt inte om du förstått hur tvåkomplement fungerar. Det handlar inte bara om att den första biten används för att indikera om talet är positivt eller negativt, utan för att konvertera ett positivt tal till negativt eller tvärtom så inverterar man alla bitar och adderar 1. Om man t.ex. använder 4 bitar så är 6 = 0110, och -6 = 1001 + 1 = 1010.