How to Convert from Binary to Decimal

David

4 years ago

We use the decimal numeral system in our daily life, which is based on 10 numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The binary numeral system, however, is based on 2 numbers: 0 and 1.

In the binary system, each digit represents an increasing power of 2 from 2⁰, 2¹, 2²…. and so on. Please refer to the table below to convert a binary number into the decimal number, or please check here to convert decimal to binary.

Power	7	6	5	4	3	2	1	0
Power of 2	2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
Results	128	64	32	16	8	4	2	1

Example 1: 01001111

01001111 = [ ( 0 ) × 2⁷ ] + [ ( 1 ) × 2⁶ ] + [ ( 0 ) × 2⁵ ] + [ ( 0 ) × 2⁴ ] + [ ( 1 ) × 2³ ] + [ ( 1 ) × 2² ] + [ ( 1 ) × 2¹ ] + [ ( 1 ) × 2⁰ ]

01001111 = 0 + 64 + 0 + 0 + 8 + 4 + 2 + 1 = 79

Example 2: 10010000

10010000 = [ ( 1 ) × 2⁷ ] + [ ( 0 ) × 2⁶ ] + [ ( 0 ) × 2⁵ ] + [ ( 1 ) × 2⁴ ] + [ (0 ) × 2³ ] + [ ( 0 ) × 2² ] + [ ( 0 ) × 2¹ ] + [ ( 0 ) × 2⁰ ]

10010000 = 128 + 0 + 0 + 16 + 0 + 0 + 0 + 0 = 144

The following is the Binary to Decimal Conversion Table from 1 to 255:

Binary	D	Binary	D	Binary	D	Binary	D
00000001	1	01000001	65	10000001	129	11000001	193
00000010	2	01000010	66	10000010	130	11000010	194
00000011	3	01000011	67	10000011	131	11000011	195
00000100	4	01000100	68	10000100	132	11000100	196
00000101	5	01000101	69	10000101	133	11000101	197
00000110	6	01000110	70	10000110	134	11000110	198
00000111	7	01000111	71	10000111	135	11000111	199
00001000	8	01001000	72	10001000	136	11001000	200
00001001	9	01001001	73	10001001	137	11001001	201
00001010	10	01001010	74	10001010	138	11001010	202
00001011	11	01001011	75	10001011	139	11001011	203
00001100	12	01001100	76	10001100	140	11001100	204
00001101	13	01001101	77	10001101	141	11001101	205
00001110	14	01001110	78	10001110	142	11001110	206
00001111	15	01001111	79	10001111	143	11001111	207
00010000	16	01010000	80	10010000	144	11010000	208
00010001	17	01010001	81	10010001	145	11010001	209
00010010	18	01010010	82	10010010	146	11010010	210
00010011	19	01010011	83	10010011	147	11010011	211
00010100	20	01010100	84	10010100	148	11010100	212
00010101	21	01010101	85	10010101	149	11010101	213
00010110	22	01010110	86	10010110	150	11010110	214
00010111	23	01010111	87	10010111	151	11010111	215
00011000	24	01011000	88	10011000	152	11011000	216
00011001	25	01011001	89	10011001	153	11011001	217
00011010	26	01011010	90	10011010	154	11011010	218
00011011	27	01011011	91	10011011	155	11011011	219
00011100	28	01011100	92	10011100	156	11011100	220
00011101	29	01011101	93	10011101	157	11011101	221
00011110	30	01011110	94	10011110	158	11011110	222
00011111	31	01011111	95	10011111	159	11011111	223
00100000	32	01100000	96	10100000	160	11100000	224
00100001	33	01100001	97	10100001	161	11100001	225
00100010	34	01100010	98	10100010	162	11100010	226
00100011	35	01100011	99	10100011	163	11100011	227
00100100	36	01100100	100	10100100	164	11100100	228
00100101	37	01100101	101	10100101	165	11100101	229
00100110	38	01100110	102	10100110	166	11100110	230
00100111	39	01100111	103	10100111	167	11100111	231
00101000	40	01101000	104	10101000	168	11101000	232
00101001	41	01101001	105	10101001	169	11101001	233
00101010	42	01101010	106	10101010	170	11101010	234
00101011	43	01101011	107	10101011	171	11101011	235
00101100	44	01101100	108	10101100	172	11101100	236
00101101	45	01101101	109	10101101	173	11101101	237
00101110	46	01101110	110	10101110	174	11101110	238
00101111	47	01101111	111	10101111	175	11101111	239
00110000	48	01110000	112	10110000	176	11110000	240
00110001	49	01110001	113	10110001	177	11110001	241
00110010	50	01110010	114	10110010	178	11110010	242
00110011	51	01110011	115	10110011	179	11110011	243
00110100	52	01110100	116	10110100	180	11110100	244
00110101	53	01110101	117	10110101	181	11110101	245
00110110	54	01110110	118	10110110	182	11110110	246
00110111	55	01110111	119	10110111	183	11110111	247
00111000	56	01111000	120	10111000	184	11111000	248
00111001	57	01111001	121	10111001	185	11111001	249
00111010	58	01111010	122	10111010	186	11111010	250
00111011	59	01111011	123	10111011	187	11111011	251
00111100	60	01111100	124	10111100	188	11111100	252
00111101	61	01111101	125	10111101	189	11111101	253
00111110	62	01111110	126	10111110	190	11111110	254
00111111	63	01111111	127	10111111	191	11111111	255
01000000	64	10000000	128	11000000	192