How to use the BIN2OCT function
The BIN2OCT function converts a binary number to octal.
What is the binary system?
The binary system is a positional numeral system that uses only two digits: 0 and 1. The binary system is important in our society, many devices like computers, digital cameras, mobile phones and modern cars use binary code to store, process and communicate data. The binary numeral system makes it easy to store and transmit data using binary digits or bits.
What is a bit?
A bit is a binary digit. It is the most basic unit of information in binary communication and computing. The bit can either be the value 0 (zero) or 1, a bit can also be part of a larger sequence of bits that can represent numbers, characters, and other types of data.
The following table shows the binary, decimal and octal values from 0 (zero) to 17.
| Binary | Decimal | Octal |
| 00000000 | 0 | 0 |
| 00000001 | 1 | 1 |
| 00000010 | 2 | 2 |
| 00000011 | 3 | 3 |
| 00000100 | 4 | 4 |
| 00000101 | 5 | 5 |
| 00000110 | 6 | 6 |
| 00000111 | 7 | 7 |
| 00001000 | 8 | 10 |
| 00001001 | 9 | 11 |
| 00001010 | 10 | 12 |
| 00001011 | 11 | 13 |
| 00001100 | 12 | 14 |
| 00001101 | 13 | 15 |
| 00001110 | 14 | 16 |
| 00001111 | 15 | 17 |
| 00010000 | 16 | 20 |
| 00010001 | 17 | 21 |
What is the octal system?
The octal system is a number system with a base of 8 that uses the digits 0, 1, 2, 3, 4, 5, 6 and 7. The octal system is often used in electronics because it is easy to perform a conversion between octal and binary numbers.
Converting between octal and binary is easy because each octal digit directly maps to a unique 3-bit binary sequence. This fixed relationship arises from the fact that ( 8 = 2^3 ), meaning each octal digit can be represented by exactly 3 binary bits.
Steps to Convert Octal to Binary
- Take each octal digit.
- Convert it to its 3-bit binary equivalent.
- Concatenate the binary groups to get the final binary number.
For example, converting octal 157 to binary:
1 in octal → 001 in binary
5 in octal → 101 in binary
7 in octal → 111 in binary
Octal 157 becomes binary 001 101 111.
Steps to Convert Binary to Octal
- Divide the binary number into groups of 3 bits, starting from the right.
- Convert each group to its octal equivalent.
- Concatenate the octal digits to get the final octal number.
For example, converting binary 1101111 to octal:
110 in binary → 6 in octal
111 in binary → 7 in octal
Binary 1101111 becomes octal 67.
Since every octal digit maps directly to a 3-bit binary sequence the conversion involves no complex calculations or regrouping like decimal-to-binary or hexadecimal-to-binary. You substitute each digit individually making it quick and straightforward.
Table of Contents
1. BIN2OCT function Syntax
BIN2OCT(number,[places])
2. BIN2OCT function Arguments
| number | Required. The binary number you want to convert to octal. The sign bit is the most significant bit of number, the following 9 bits are magnitude bits. Negative numbers are represented using two's-complement notation. Maximum binary values are 10 characters. |
| [places] | Optional. The number of characters to use. If not entered the minimum number of characters is used. Use this argument to add leading 0 (zeros). |
What is a sign bit?
The sign bit indicates whether a binary number is positive or negative, if the bit is 0 the number is positive, if the bit is 1, the number is negative.
What is a magnitude bit?
The remaining 9 bits are magnitude bits which represents the absolute value of the number. An absolute number is a number without the sign.
What is two's-complement notation?
Two’s-complement notation is used to represent negative numbers, the magnitude bits are changed from 0 to 1 and 1 to 0 and adding 1 to the result. For example:
Decimal number +9 using 10 bits is 0000001001.
Decimal number -9 using 10 bits is 1111110110 + 1 = 1111110111
3. BIN2OCT function example
The image above shows the BIN2OCT function in cells C3, C4, C5, and C6. It calculates the octal values based on the corresponding cells which contain different binary numbers.
Formula in cell C3:
The first cell B3 contains 0000011001 and the BIN2OCT function returns 31 in cell C3, the second cell B4 contains 0000000011 and the BIN2OCT function returns 3.
The third cell B5 contains 0000000100 and the BIN2OCT function returns 4 in cell C3, the fifth cell B6 contains 0011111111 and the BIN2OCT function returns 377.
The next section describes how these values are calculated in detail.
4. How is the BIN2OCT function calculated in detail?
Follow these steps in order to convert from binary to octal:
-
- Divide the binary number into groups of three bits starting from the rightmost bit.
- Add leading zeros to make it a full group if the leftmost group contains less than three bits.
- Find the corresponding octal digit for each group using this table:
| Binary | Decimal | Octal |
| 000 | 0 | 0 |
| 001 | 1 | 1 |
| 010 | 2 | 2 |
| 011 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
- Write the octal digits in the same order as the binary groups.
5. BIN2OCT function not working
BIN2OCT returns the #NUM! error value if
- more than 10 binary digits are used. See cells B3 and C3 in the image above.
- the number is not a valid binary number. See cells B4 and C4 in the image above.
- [places] is negative. See the formula next to cell C5.
- it requires more than the specified places characters. See the formula next to cell C6.
BIN2OCT returns the #VALUE! error value if places is not a number. See the formula next to cell C7.
The second argument [places]is truncated if it is not an integer. For example, [places] is 4.5 and the BIN2OCT function truncates it to 4. See the formula next to cell C8.
BIN2OCT ignores places and returns a 10-character hexadecimal number if the binary number is negative.
Useful links
BIN2OCT function - Microsoft
Octal numeral system - Wikipedia
Octal Number System - Meaning, Conversion, Solved Examples, Practice Questions (cuemath.com)
'' function examples
The following article has a formula that contains the function.
Functions in 'Engineering' category
The BIN2OCT function function is one of 42 functions in the 'Engineering' category.
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