Binary Number Base Conversions
Learn how to convert binary numbers in Excel using BIN2DEC, DEC2BIN, and BIN2HEX. Understand the 10-character limit, two's complement, and bit padding cleanly.
Hardware engineers, network analysts, and PLC programmers frequently work with raw register bitstrings from industrial microcontrollers and network packets. Status registers report telemetry as 8-bit binary strings (like "10101000").
To compute physical sensor values, engineers convert these binary numbers into Base-10 decimals. To match firmware memory maps, they convert them into Base-16 hexadecimal notation. Excel provides a dedicated set of conversion formulas: BIN2DEC, BIN2HEX, and DEC2BIN.
Quick Comparison: Binary Conversion Family
| Formula | Input Base | Output Base | Max Input Size | Best Fit in Real Work |
|---|---|---|---|---|
BIN2DEC(number) |
Base-2 (Binary) | Base-10 (Decimal) | 10 characters (signed) | Converting microcontroller flags into sensor values. |
BIN2HEX(number, [places]) |
Base-2 (Binary) | Base-16 (Hexadecimal) | 10 characters | Mapping bit patterns to memory addresses. |
DEC2BIN(number, [places]) |
Base-10 (Decimal) | Base-2 (Binary) | -512 to +511 | Encoding configuration integers into hardware bitmasks. |
Deep Technical Constraints
1. The 10-Character Binary Limit
Excel binary conversion formulas have a strict 10-bit limitation. Of these 10 bits, 9 bits represent the number value and the 10th bit (the most significant bit on the far left) acts as the negative sign bit.
- Maximum positive binary value:
0111111111(decimal511). - Minimum negative binary value:
1000000000(decimal-512). - Passing more than 10 characters immediately throws a
#NUM!error.
2. Two's Complement Interpretation
When the 10th bit is 1, Excel evaluates the number using two's complement notation. For example, BIN2DEC("1111111111") returns -1, not 1023!
3. Zero-Padding with the [places] Argument
When converting from decimal to binary with DEC2BIN, use the optional second argument to pad the output with leading zeros so it fits standard byte widths: =DEC2BIN(9, 8) returns "00001001".
Hands-on Practice Playground
Use the PLC telemetry table below to convert binary register codes. Follow each objective to complete the exercise.
In cell C2, convert the binary string in B2 into a decimal integer.
In cell C2, convert the binary telemetry string in B2 into its Base-10 decimal integer using the BIN2DEC formula.
In cell D2, convert the binary string into hexadecimal notation.
In cell D2, convert binary telemetry string B2 into hexadecimal notation using the BIN2HEX formula.
In cell E2, convert the decimal value from C2 back into an 8-bit padded binary string.
In cell E2, convert the decimal value from C2 back into an 8-bit binary string padded with leading zeros using DEC2BIN with places set to 8.
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