Why does the same byte value look different in binary, decimal, and hexadecimal?

They are three notations for the same numeric value, not three different values. In a Microsoft .NET Byte example, decimal 104 is shown as hexadecimal 68 and binary 1101000; adding a leading zero gives the eight-digit binary form 01101000 [S1].

Each notation uses a different base. Decimal uses powers of 10, binary uses powers of 2, and hexadecimal uses powers of 16. In 01101000, the place values from left to right are 128, 64, 32, 16, 8, 4, 2, and 1. The 1 digits mark 64, 32, and 8; together, those add to 104.

The written digits change, but the value they represent stays the same.

Here is one byte written three ways:

• Binary: 01101000 = 64 + 32 + 8 = 104
• Decimal: 104 = one hundred four
• Hexadecimal: 68 = 6 × 16 + 8 = 104

The binary form uses eight digits to make the byte width visible; its first zero contributes nothing to the total. In hexadecimal, the 6 is in the sixteens place and the 8 is in the ones place. This conversion matches the .NET example [S1].

This shows equivalent notations; it does not mean every program displays bytes in all three formats by default. Formatting can determine which notation you see.

No. 1101000 and 01101000 have the same value: the first leaves out a leading zero, while the second shows it explicitly. The .NET example shows both forms for decimal 104 [S1].

Eight binary digits can make a byte-width display easy to count. A leading zero is padding in the written form, not a change to the numeric value. When comparing values, leading zeros do not affect the total; when checking how a byte is displayed, count the digits shown. Those are two different questions: “What number is this?” and “How many digits does this display include?”

First identify the base from its label or context; the digits alone may not make that clear. Then convert it to a value you can check. For binary, add the place values wherever the digit is 1. For hexadecimal, multiply each digit by its place value, counting from the right in powers of 16. Compare the totals.

For this example, binary 01101000 gives 64 + 32 + 8 = 104; hexadecimal 68 gives 6 × 16 + 8 = 104; and decimal is 104 [S1]. These notations represent the same value. The cited example does not establish how a particular device, file viewer, or programming language will display a byte. If a display is unexpected, check that tool’s format or documentation.