How to use the BIN2OCT function

What is the BIN2OCT function?

The BIN2OCT function converts a binary number to octal.

1. Introduction

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

1.  Take each octal digit.
2. Convert it to its 3-bit binary equivalent.
3. 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

1. Divide the binary number into groups of 3 bits, starting from the right.
2. Convert each group to its octal equivalent.
3. 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.

2. Syntax

BIN2OCT(number,[places])

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

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3. 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.

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4. How is the function calculated in detail?

Follow these steps in order to convert from binary to octal:

1. 1. Divide the binary number into groups of three bits starting from the rightmost bit.
   2. Add leading zeros to make it a full group if the leftmost group contains less than three bits.
   3. 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

1. Write the octal digits in the same order as the binary groups.

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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.

5.1 Troubleshooting the error value

When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.

1. The first line describes the error if you press with left mouse button on it.
2. The second line opens a pane that explains the error in greater detail.
3. The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
4. This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
5. The fifth line lets you edit the formula in the Formula bar.
6. The sixth line opens the Excel settings so you can adjust the Error Checking Options.

Here are a few of the most common Excel errors you may encounter.

#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.

#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.

#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.

#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.

#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.

#NAME error - The #NAME error happens if you misspelled a function or a named range.

#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.

#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.

#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.

5.2 The formula returns an unwanted value

To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that Here is how to troubleshoot a formula:

1. Select the cell containing the formula you want to examine in detail.
2. Go to tab “Formulas” on the ribbon.
3. Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
   The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control.
4. Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
5. Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
6. Press "Close" button to dismiss the dialog box.

There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..

1. Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
2. Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
3. Press F9: This will calculate and display the result of just that selected portion.
4. Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
5. Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.

The image above shows cell reference B3 converted to hard-coded value using the F9 key. The BIN2OCT function requires a binary number input value smaller than 11 digits. We have found what is wrong with the formula using the F9 key.

Tips!

• View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
• Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
• Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.

Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button

Other errors

Floating-point arithmetic may give inaccurate results in Excel - Article

Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.

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Useful links

BIN2OCT function - Microsoft
Octal numeral system - Wikipedia
Octal Number System - Meaning, Conversion, Solved Examples, Practice Questions (cuemath.com)

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Functions in 'Engineering' category

The BIN2OCT function function is one of 42 functions in the 'Engineering' category.

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