How to make the calculation from Hexadecimal to Decimal

Objective

Steps

Hex is a base 16 number and decimal is a base 10 number. Reference the hexadecimal to decimal chart below to determine the decimal equivalent of every hexadecimal digit.

Here are the steps to convert hexadecimal to decimal:

Get the decimal equivalent of hexadecimal value from chart below.
Multiply every digit with a 16 power based on the digit location.
(zero based, 7DE: E location is 0, D location is 1 and the 7 location is 2)
Sum all the multipliers.

Here is an example:

7DE is a hex number
7DE = (7 * 16²) + (13 * 16¹) + (14 * 16⁰)
7DE = (7 * 256) + (13 * 16) + (14 * 1)
7DE = 1792 + 208 + 14
7DE = 2014 (in decimal number)

16 Bit Factor Table:

16⁰ = 1

16¹ = 16

16² = 256

16³ = 4096

Decimal System

Decimal number system is the most commonly used and the most familiar one to the general public. It is also known as Base 10 numbering system since it is based on 10 following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In decimal system, every digit has its own position as well as the decimal point. I.E. the number 356.74 has 4 in the Hundredths position, 7 in the Tenths position, 6 in the Units position, 5 in the Tens position, and 3 in the Hundreds position. Decimal number system is also one of the oldest known numeral systems, which is historically related to Hindu-Arabic numeral system.

Hex System

Hex, or hexadecimal, is a number system of base 16. This number system is especially interesting because while the decimal system uses only 10 digits to represent numbers, the hex system uses 16 digits. The extra needed 6 digits are represented by the first 6 letters of English alphabet. Hence, hex digits are 0,1,2,3,4,5,6,7,8, 9 and A, B, C, D, E, F. This number system is the most commonly used in mathematics and information technologies. I.e. in html, programming colors can be represented by a 6-digit hexadecimal number (FFFFFF represents white and 000000 represents black).

Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin
0	0	0	0	16	10	20	10000	32	20	40	100000	48	30	60	110000
1	1	1	1	17	11	21	10001	33	21	41	100001	49	31	61	110001
2	2	2	10	18	12	22	10010	34	22	42	100010	50	32	62	110010
3	3	3	11	19	13	23	10011	35	23	43	100011	51	33	63	110011
4	4	4	100	20	14	24	10100	36	24	44	100100	52	34	64	110100
5	5	5	101	21	15	25	10101	37	25	45	100101	53	35	65	110101
6	6	6	110	22	16	26	10110	38	26	46	100110	54	36	66	110110
7	7	7	111	23	17	27	10111	39	27	47	100111	55	37	67	110111
8	8	10	1000	24	18	30	11000	40	28	50	101000	56	38	70	111000
9	9	11	1001	25	19	31	11001	41	29	51	101001	57	39	71	111001
10	A	12	1010	26	1A	32	11010	42	2A	52	101010	58	3A	72	111010
11	B	13	1011	27	1B	33	11011	43	2B	53	101011	59	3B	73	111011
12	C	14	1100	28	1C	34	11100	44	2C	54	101100	60	3C	74	111100
13	D	15	1101	29	1D	35	11101	45	2D	55	101101	61	3D	75	111101
14	E	16	1110	30	1E	36	11110	46	2E	56	101110	62	3E	76	111110
15	F	17	1111	31	1F	37	11111	47	2F	57	101111	63	3F	77	111111

Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin
64	40	100	1000000	80	50	120	1010000	96	60	140	1100000	112	70	160	1110000
65	41	101	1000001	81	51	121	1010001	97	61	141	1100001	113	71	161	1110001
66	42	102	1000010	82	52	122	1010010	98	62	142	1100010	114	72	162	1110010
67	43	103	1000011	83	53	123	1010011	99	63	143	1100011	115	73	163	1110011
68	44	104	1000100	84	54	124	1010100	100	64	144	1100100	116	74	164	1110100
69	45	105	1000101	85	55	125	1010101	101	65	145	1100101	117	75	165	1110101
70	46	106	1000110	86	56	126	1010110	102	66	146	1100110	118	76	166	1110110
71	47	107	1000111	87	57	127	1010111	103	67	147	1100111	119	77	167	1110111
72	48	110	1001000	88	58	130	1011000	104	68	150	1101000	120	78	170	1111000
73	49	111	1001001	89	59	131	1011001	105	69	151	1101001	121	79	171	1111001
74	4A	112	1001010	90	5A	132	1011010	106	6A	152	1101010	122	7A	172	1111010
75	4B	113	1001011	91	5B	133	1011011	107	6B	153	1101011	123	7B	173	1111011
76	4C	114	1001100	92	5C	134	1011100	108	6C	154	1101100	124	7C	174	1111100
77	4D	115	1001101	93	5D	135	1011101	109	6D	155	1101101	125	7D	175	1111101
78	4E	116	1001110	94	5E	136	1011110	110	6E	156	1101110	126	7E	176	1111110
79	4F	117	1001111	95	5F	137	1011111	111	6F	157	1101111	127	7F	177	1111111

Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin
128	80	200	10000000	144	90	220	10010000	160	A0	240	10100000	176	B0	260	10110000
129	81	201	10000001	145	91	221	10010001	161	A1	241	10100001	177	B1	261	10110001
130	82	202	10000010	146	92	222	10010010	162	A2	242	10100010	178	B2	262	10110010
131	83	203	10000011	147	93	223	10010011	163	A3	243	10100011	179	B3	263	10110011
132	84	204	10000100	148	94	224	10010100	164	A4	244	10100100	180	B4	264	10110100
133	85	205	10000101	149	95	225	10010101	165	A5	245	10100101	181	B5	265	10110101
134	86	206	10000110	150	96	226	10010110	166	A6	246	10100110	182	B6	266	10110110
135	87	207	10000111	151	97	227	10010111	167	A7	247	10100111	183	B7	267	10110111
136	88	210	10001000	152	98	230	10011000	168	A8	250	10101000	184	B8	270	10111000
137	89	211	10001001	153	99	231	10011001	169	A9	251	10101001	185	B9	271	10111001
138	8A	212	10001010	154	9A	232	10011010	170	AA	252	10101010	186	BA	272	10111010
139	8B	213	10001011	155	9B	233	10011011	171	AB	253	10101011	187	BB	273	10111011
140	8C	214	10001100	156	9C	234	10011100	172	AC	254	10101100	188	BC	274	10111100
141	8D	215	10001101	157	9D	235	10011101	173	AD	255	10101101	189	BD	275	10111101
142	8E	216	10001110	158	9E	236	10011110	174	AE	256	10101110	190	BE	276	10111110
143	8F	217	10001111	159	9F	237	10011111	175	AF	257	10101111	191	BF	277	10111111

Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin	Dec	Hex	Oct	Bin
192	C0	300	11000000	208	D0	320	11010000	224	E0	340	11100000	240	F0	360	11110000
193	C1	301	11000001	209	D1	321	11010001	225	E1	341	11100001	241	F1	361	11110001
194	C2	302	11000010	210	D2	322	11010010	226	E2	342	11100010	242	F2	362	11110010
195	C3	303	11000011	211	D3	323	11010011	227	E3	343	11100011	243	F3	363	11110011
196	C4	304	11000100	212	D4	324	11010100	228	E4	344	11100100	244	F4	364	11110100
197	C5	305	11000101	213	D5	325	11010101	229	E5	345	11100101	245	F5	365	11110101
198	C6	306	11000110	214	D6	326	11010110	230	E6	346	11100110	246	F6	366	11110110
199	C7	307	11000111	215	D7	327	11010111	231	E7	347	11100111	247	F7	367	11110111
200	C8	310	11001000	216	D8	330	11011000	232	E8	350	11101000	248	F8	370	11111000
201	C9	311	11001001	217	D9	331	11011001	233	E9	351	11101001	249	F9	371	11111001
202	CA	312	11001010	218	DA	332	11011010	234	EA	352	11101010	250	FA	372	11111010
203	CB	313	11001011	219	DB	333	11011011	235	EB	353	11101011	251	FB	373	11111011
204	CC	314	11001100	220	DC	334	11011100	236	EC	354	11101100	252	FC	374	11111100
205	CD	315	11001101	221	DD	335	11011101	237	ED	355	11101101	253	FD	375	11111101
206	CE	316	11001110	222	DE	336	11011110	238	EE	356	11101110	254	FE	376	11111110
207	CF	317	11001111	223	DF	337	11011111	239	EF	357	11101111	255	FF	377	11111111

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