Negative Numbers

Negative Numbers
Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex
-128	80	-127	81	-126	82	-125	83	-124	84	-123	85	-122	86	-121	87
-120	88	-119	89	-118	8A	-117	8B	-116	8C	-115	8D	-114	8E	-113	8F
-112	90	-111	91	-110	92	-109	93	-108	94	-107	95	-106	96	-105	97
-104	98	-103	99	-102	9A	-101	9B	-100	9C	-099	9D	-098	9E	-097	9F
-096	A0	-095	A1	-094	A2	-093	A3	-092	A4	-091	A5	-090	A6	-089	A7
-088	A8	-087	A9	-086	AA	-085	AB	-084	AC	-083	AD	-082	AE	-081	AF
-080	B0	-079	B1	-078	B2	-077	B3	-076	B4	-075	B5	-074	B6	-073	B7
-072	B8	-071	B9	-070	BA	-069	BB	-068	BC	-067	BD	-066	BE	-065	BF
-064	C0	-063	C1	-062	C2	-061	C3	-060	C4	-059	C5	-058	C6	-057	C7
-056	C8	-055	C9	-054	CA	-053	CB	-052	CC	-051	CD	-050	CE	-049	CF
-048	D0	-047	D1	-046	D2	-045	D3	-044	D4	-043	D5	-042	D6	-041	D7
-040	D8	-039	D9	-038	DA	-037	DB	-036	DC	-035	DD	-034	DE	-033	DF
-032	E0	-031	E1	-030	E2	-029	E3	-028	E4	-027	E5	-026	E6	-025	E7
-024	E8	-023	E9	-022	EA	-021	EB	-020	EC	-019	ED	-018	EE	-017	EF
-016	F0	-015	F1	-014	F2	-013	F3	-012	F4	-011	F5	-010	F6	-009	F7
-008	F8	-007	F9	-006	FA	-005	FB	-004	FC	-003	FD	-002	FE	-001	FF
Positive Numbers
Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex
+000	00	+001	01	+002	02	+003	03	+004	04	+005	05	+006	06	+007	07
+008	08	+009	09	+010	0A	+011	0B	+012	0C	+013	0D	+014	0E	+015	0F
+016	10	+017	11	+018	12	+019	13	+020	14	+021	15	+022	16	+023	17
+024	18	+025	18	+026	1A	+027	1B	+028	1C	+029	1D	+030	1E	+031	1F
+032	20	+033	21	+034	22	+035	23	+036	24	+037	25	+038	26	+039	27
+040	28	+041	29	+042	2A	+043	2B	+044	2C	+045	2D	+046	2E	+047	2F
+048	30	+049	31	+050	32	+051	33	+052	34	+053	35	+054	36	+055	37
+056	38	+057	39	+058	3A	+059	3B	+060	3C	+061	3D	+062	3E	+063	3F
+064	40	+065	41	+066	42	+067	43	+068	44	+069	45	+070	46	+071	47
+072	48	+073	49	+074	4A	+075	4B	+076	4C	+077	4D	+078	4E	+079	4F
+080	50	+081	51	+082	52	+083	53	+084	54	+085	55	+086	56	+087	57
+088	58	+089	59	+090	5A	+091	5B	+092	5C	+093	5D	+094	5E	+095	5F
+096	60	+097	61	+098	63	+099	63	+100	64	+101	65	+102	66	+103	67
+104	68	+105	69	+106	6A	+107	6B	+108	6C	+109	6D	+110	6E	+111	6F
+112	70	+113	71	+114	72	+115	73	+116	74	+117	75	+118	76	+119	77
+120	78	+121	79	+122	7A	+123	7B	+124	7C	+125	7D	+126	7E	+127	7F

Two's complement

The numbers work as follows.

The leftmost bit in an eight bit byte is the sign bit.

    1 0 1 0 1 0 1 0
    ^ 
    ^ The sign bit has a value of -128 decimal or -80 hexadecimal.

The other seven bits are treated as a normal positive number between 0 and 127. This is true whether the overall number is positive or negative. For example to store -1 the binary is

    1 1 1 1 1 1 1 1     - 128d + 127d = -1d
    ^
    ^ -128d

To store 127 decimal, the binary is

    0 1 1 1 1 1 1 1     0 + 127d = 127d
    ^
    ^ The sign bit is zero.

16 and 32 bit machines also use the leftmost bit as the sign bit. The negative numbers work in exactly the same way but much bigger niumbers can be stored. In a 16 bit machine, the sign bit is worth -32768. In a 32 bit machine, the sign bit is worth -2147483648 (2000 million approximately).

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Negative Numbers

Negative Numbers

Positive Numbers

Two's complement