The go to open source product on Linux (and everything else) is Radare which provides radiff2 explicitly for this purpose. I voted to close this because myself and others have the same question, in the question you ask

for every different byte

That's insane though. Because as asked, if you insert one byte at the first byte in the file, you'd find every subsequent byte was different and so the diff would repeat the whole file, for an actual difference of one byte.

Slightly more practical is radiff -O. The -O is for ""Do code diffing with all bytes instead of just the fixed opcode bytes""

0x000000a4 0c01 => 3802 0x000000a4
0x000000a8 1401 => 3802 0x000000a8
0x000000ac 06 => 05 0x000000ac
0x000000b4 02 => 01 0x000000b4
0x000000b8 4c05 => 0020 0x000000b8
0x000000bc 4c95 => 00a0 0x000000bc
0x000000c0 4c95 => 00a0 0x000000c0

Like IDA Pro, Radare is a tool primary for binary analysis, you can also show delta diffing with -d, or display the disassembled bytes instead of hex with -D.

If you're asking these kind of questions though, check out

• Stack Overflow for the software questions,
• Reverse Engineering Stack Exchange
• Radare's radiff2 for binary diffing

The go to open source product on Linux (and everything else) is Radare which provides radiff2 explicitly for this purpose.

for every different byte

That's insane though. Because as asked, if you insert one byte at the first byte in the file, you'd find every subsequent byte was different and so the diff would repeat the whole file, for an actual difference of one byte.

Slightly more practical is radiff -O. The -O is for ""Do code diffing with all bytes instead of just the fixed opcode bytes""

0x000000a4 0c01 => 3802 0x000000a4
0x000000a8 1401 => 3802 0x000000a8
0x000000ac 06 => 05 0x000000ac
0x000000b4 02 => 01 0x000000b4
0x000000b8 4c05 => 0020 0x000000b8
0x000000bc 4c95 => 00a0 0x000000bc
0x000000c0 4c95 => 00a0 0x000000c0

Like IDA Pro, Radare is a tool primary for binary analysis, and you can also show delta diffing with -d, or display the disassembled bytes instead of hex with -D.

See also:

• Radare's radiff2 for binary diffing