Binary To Octal Conversion

Share

Tweet

Share

Share

Email

Comments

In binary to octal conversion, we only learn how the base 2 is converted into base 8 number system. The binary to octal conversion is not directly take place. Digital computer can only understand the binary number. At the same time the octal number is also use in electronics computer. In this tutorial we are learn about the binary to octal conversion.
Binary is the simples type of number that use only two digits one is “0” and other is “0” (i.e. value of base 2). The digital electronics only use two states either it is 0 or 1. In modern day computer the binary number use widely. It is also use in communication and other type of professionals.

“Whereas octal number is one of another type of number system. In which have 10 values and it has only 8 symbols that are 0 to 7”.

What are Binary Numbers?

The binary number system only uses two state that are “0” and “1”.the radix have 2. This number is the primer language of digital computer system. Some example of binary number is (111110)_2, (1111111)_2, (1011001)_2.

What are Octal numbers?

In octal number system having 8 number which is  0,1,2,3,4,5,6,7. And the radix of this number system is 8. This number was use in ancient of some Native American tribes until 20^th century. This number is popular in early age of computing as a language of computer programming. because of shorten of binary number by simplifying long and complex chains of binary displays used by computers.
This number is manly use for binary counting in group forms. The representation of octal number is grouping of three binary bits. Since 8 are 2 to the third power 2³.

Conversion from Binary to Octal number system

The conversion of binary to octal number is easy because octal number has specified value of binary numbers. You just have to remember that each octal value in to three binary bits. You can follow the steps to convert binary to octal number system.

• Step 1: Write down the binary digits and group of three bit. Start doing this from the right. If the leftmost group doesn’t have enough digits to make up a set of three, add extra 0’s to make another group.
• Step 2: Write decimal value 4, 2 and 1 below each group. These are the weights that the positions carry (2², 2¹, 2⁰).
• Step 3: Every three group of binary bit will give you one digit in octal number.
• Step 4: Add the products.
• Step 5: The sums will give you the octal number; it is from left to right.

Step 1: 111010 has six binary bit and therefore can be grouped in sets of three.
Think of the number as (111)(010).

Step 2: Write decimal value 4,2 and 1 below each binary bit group.

111    010
421    421

Step 3: Multiply the 4, 2 and 1’s with the binary bit above.

111    010
421    421

Step 4: Add the products.

In the first group, 4 + 2 + 1 = 7
In the second group, 0 + 2 + 0 = 2

111    010
421    421
7      2

Step 5: (111010)₂  = (72)₈

Binary to Octal Conversion Examples

Example 1: (1010001)₂ = (121)₈
(1)(010)(001)
Here the all bit cannot group all in three. Add two extra bit “0” to from grouping of three bit and repeat the above step.

001     010     001
421     421     421
1        2          1

And result is 121

Example 1: Convert (1010101)₂ to octal

Solution:
Given binary number are (1010101)₂
First, we convert given binary to decimal
1010101₂ = (1 * 2⁶) + (0 * 2⁵ ) + (1 * 2⁴) + (0 * 2³) + (1 * 2²) + (0 * 2¹) + (1 * 2⁰)
= 64 + 0 + 16 + 0 + 4 + 0 + 1
= 64 + 21
010101₂= 85 (Decimal form)

Therefore, the equivalent octal number is (125)₈.

Example 2: Convert (01101)₂ to octal

Solution:
Given binary number are (01101)₂
First we convert given binary to decimal
01101₂ = (0 * 2⁴) + (1 * 2³) + (1 * 2³) + (0 * 2) + (1 *2⁰)
= 0 + 8 + 4 + 0 +1
01101₂= 13 (Decimal form)

Therefore, the equivalent octal number is (15)₈.

Binary Octal Conversion Chart Table

Binary	Octal	Binary	Octal	Binary	Octal	Binary	Octal
00000001	1	01000001	101	10000001	201	11000001	301
00000010	2	01000010	102	10000010	202	11000010	302
00000011	3	01000011	103	10000011	203	11000011	303
00000100	4	01000100	104	10000100	204	11000100	304
00000101	5	01000101	105	10000101	205	11000101	305
00000110	6	01000110	106	10000110	206	11000110	306
00000111	7	01000111	107	10000111	207	11000111	307
00001000	10	01001000	110	10001000	210	11001000	310
00001001	11	01001001	111	10001001	211	11001001	311
00001010	12	01001010	112	10001010	212	11001010	312
00001011	13	01001011	113	10001011	213	11001011	313
00001100	14	01001100	114	10001100	214	11001100	314
00001101	15	01001101	115	10001101	215	11001101	315
00001110	16	01001110	116	10001110	216	11001110	316
00001111	17	01001111	117	10001111	217	11001111	317
00010000	20	01010000	120	10010000	220	11010000	320
00010001	21	01010001	121	10010001	221	11010001	321
00010010	22	01010010	122	10010010	222	11010010	322
00010011	23	01010011	123	10010011	223	11010011	323
00010100	24	01010100	124	10010100	224	11010100	324
00010101	25	01010101	125	10010101	225	11010101	325
00010110	26	01010110	126	10010110	226	11010110	326
00010111	27	01010111	127	10010111	227	11010111	327
00011000	30	01011000	130	10011000	230	11011000	330
00011001	31	01011001	131	10011001	231	11011001	331
00011010	32	01011010	132	10011010	232	11011010	332
00011011	33	01011011	133	10011011	233	11011011	333
00011100	34	01011100	134	10011100	234	11011100	334
00011101	35	01011101	135	10011101	235	11011101	335
00011110	36	01011110	136	10011110	236	11011110	336
00011111	37	01011111	137	10011111	237	11011111	337
00100000	40	01100000	140	10100000	240	11100000	340
00100001	41	01100001	141	10100001	241	11100001	341
00100010	42	01100010	142	10100010	242	11100010	342
00100011	43	01100011	143	10100011	243	11100011	343
00100100	44	01100100	144	10100100	244	11100100	344
00100101	45	01100101	145	10100101	245	11100101	345
00100110	46	01100110	146	10100110	246	11100110	346
00100111	47	01100111	147	10100111	247	11100111	347
00101000	50	01101000	150	10101000	250	11101000	350
00101001	51	01101001	151	10101001	251	11101001	351
00101010	52	01101010	152	10101010	252	11101010	352
00101011	53	01101011	153	10101011	253	11101011	353
00101100	54	01101100	154	10101100	254	11101100	354
00101101	55	01101101	155	10101101	255	11101101	355
00101110	56	01101110	156	10101110	256	11101110	356
00101111	57	01101111	157	10101111	257	11101111	357
00110000	60	01110000	160	10110000	260	11110000	360
00110001	61	01110001	161	10110001	261	11110001	361
00110010	62	01110010	162	10110010	262	11110010	362
00110011	63	01110011	163	10110011	263	11110011	363
00110100	64	01110100	164	10110100	264	11110100	364
00110101	65	01110101	165	10110101	265	11110101	365
00110110	66	01110110	166	10110110	266	11110110	366
00110111	67	01110111	167	10110111	267	11110111	367
00111000	70	01111000	170	10111000	270	11111000	370
00111001	71	01111001	171	10111001	271	11111001	371
00111010	72	01111010	172	10111010	272	11111010	372
00111011	73	01111011	173	10111011	273	11111011	373
00111100	74	01111100	174	10111100	274	11111100	374
00111101	75	01111101	175	10111101	275	11111101	375
00111110	76	01111110	176	10111110	276	11111110	376
00111111	77	01111111	177	10111111	277	11111111	377
01000000	100	10000000	200	11000000	300

People also ask

What is octal equivalent of the binary number 1011 1101?

Binary to Octal conversion table

Binary Number	Octal Number
1010	12
1011	13
1100	14
1101	15

What is the octal equivalent of binary number 10111101?

The binary number 10111101 is equivalent to 571
101  111  001
5      7       1

What is binary and octal?

The octal and binary number are used to write a number using different rule other than decimal number. In binary number system we only use two binary bit i.e. “0” and “1” but in octal number system we use eight number and that number is 0,1,2,3,4,5,6 and 7.

What is the octal equivalent for the binary value of 00001111?

Binary Octal Conversion Chart Table

Binary	Octal
00001110	16
00001111	17
00010000	20
00010001	21

What is the octal equivalent of hexadecimal 14?

Octal equivalent of hexadecimal 14 is 1100
Hex to Octal Conversion Table

Hexadecimal	Octal	Equivalent Binary
B	13	1011
C	14	1100
D	15	1101
E	16	1110

What is the binary equivalent of decimal number 12?

binary equivalent of decimal number 12 is 1100
Decimal to Binary Table

Decimal Number	Binary Number
11	1011
12	1100
13	1101
14	1110

Also read :- Binary addition, Binary subtraction, Binary number, Binary division.