Convert Octal To Binary | How to Convert Octal To Binary

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In order to convert octal to binary number system we have some rule. In convert to octal to binary article we are going to discuss about what are the rule we follow and everything. Firstly, what is octal number? The octal number is the part of number system in digital electronics. In digital number there are four type of number that are decimal number, binary number, octal number, hexadecimal number. The octal number have eight number and base is 8, but the binary contain only two number and that number is “0” and “1”. The base of binary is 2.

In convert octal to binary, we convert octal number to decimal number and this decimal number convert to binary equivalent number. We can also remember the octal to binary conversion table so we can quickly convert octal to binary number system. Before we understand conversion method, let us understand about both number systems.

Octal Numbers: The octal number system are that number whose base is 8 and it contains only eight numbers and that number is 0, 1, 2, 3, 4, 5, 6 and 7. These numbers are using to represents the octal number system. . For example:

• 112₈
• 1008₈
• 789₈, etc.

Binary Numbers: The binary number systems are that number whose base is 2. The binary number contains only two bits that bits are “0” and “1”. The binary number system is widely use in digital electronics, communication and various thing. Fro storing information in memory we use binary number system. . For example:

• 0011₂
• 111101₂
• 101010₂

How to Convert Octal To Binary?

The conversion of octal to binary number we use two step. First we convert octal number to decimal number and this decimal number is converting into binary number. Let us completely learn step by step here.

Octal to Decimal Conversion

1. Count the octal number present in the given number. Let the total number is ‘n’.
2. Multiply each octal digit number with 8^n-1. The 8^n-1 is for n^th position from the right end of the number. If the number has a decimal part, multiply each digit in the decimal part by `8<sup>-m</sup>` when the digit is in the m^th position from the decimal point.
3. Add all after multiplication.
4. We obtained the equivalent decimal number.

Decimal to Binary Conversion

1. The decimal numbers divide it by 2.
2. Note down the remainder.
3. Continue the above two steps till the quotient is zero or one.
4. Write down the remainder in the reverse order.
5. The reverse order is the binary equivalent number of given octal number.

Conversion of octal to binary 

Conversion of octal to binary in point form

Solved Examples

Q.1: Convert 41₈ to a binary number.

Solution: Given octal number is (41)₈
(41)₈ = [4 * 8¹] + [1 * 8⁰]
= [4 * 8 ]+ [1 * 1]
= 32+1
= 33(Decimal number)
Now convert this decimal number into binary equivalent number which is given below.

Decimal Number divided by 2	Quotient	Remainder
33 divided by 2	16	1
16 divided by 2	8	0
8 divided by 2	4	0
4 divided by 2	2	0
2 divided by 2	1	0
1 divided by 2	0	1

Therefore, the equivalent binary number is 100001₂.
Hence, (41)₈ = (100001)₂

Q.2: Convert (10)₈ to a binary number.

Solution: Given octal number are (10)₈
10₈ = [1 * 8¹] + [0 * 8⁰]
= [1 * 8] + [0 * 1]
= 8 + 0
= 8 (Decimal number)
Now convert this decimal number into binary equivalent number which is given below.

Decimal Number divided by 2	Quotient	Remainder
8 divided by 2	4	0
4 divided by 2	2	0
2 divided by 2	1	0
1 divided by 2	0	1

Therefore, the equivalent binary number is 1000₂.
Hence, (10)₈ = (1000)₂

Example: Convert (12)₈ into a binary number.

Solution: Given octal number are (12)₈.
We take help of binary table, we can write octal number;
12₈ = (001 010)₂
Since zeros is present on the left, we discard the zero because it does not have any significance. Thus,
12₈ = (1010)₂

Practice Questions

1. Convert (122)₈into binary number.
2. Convert the octal number (200)₈into binary number.
3. Convert (98)₈to a binary number.

Convert Octal to Binary

Converting from octal to binary number has a simple method because octal number is a shortened version of binary string. Always remember the all octal digits represent three binary string of bit. Therefore, one octal number gives three binary bits. While octal number can also be converting by converting into digital and this digital convert into binary. Here a direct method to convert octal to binary is given below in step by step.

• Step 1: Write down the octal number. Each octal digit represents three binary number bits.
• Step 2: Write down the each octal number into binary from in three bits string.
• Step 3: Read 1’s and 0’s you just wrote from left to right. You will get your binary number.

Some example of octal to binary conversion

Convert the octal number (456)₈ into binary number
Step 1:
Octal number =      4           5         6
Binary number = 100          101     110
Step 2:
(456)₈ = (1010011100)₂

Example 1: (1234)₈ = (001010011100) ₂

1         2         3         4
001     010     011     100

Example 2: (75426) ₈ = (111101100010110) ₂

7         5         4         2         6
111     101     100     010     110

Example 3: (6574.73) ₈ = (110101111100.111011) ₂

6         5         7         4.        7         3
110     101     111     100.    111     011

Binary to Octal Converter

Convert Octal to Binary Using Table

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

Also read:- Binary to octal conversion.