More about comparing signed integers

For CMP AX,BX the CPU computes AX-BX and sets the flags.
JS and JL are different.

The Sign bit (S) will be set if the result of AX-BX has a 1 at the most significant bit of the result (i.e., 15th bit for 16-bit op)
The Overflow flag (O) will be set if the result of AX-BX produced a number that was either too + or too - to be represented by an integer.
The conditional jump JS just looks as the sign bit (S) of the last compare (or subtraction). If 1, it jumps.
The conditional jump JL compares any two signed integers. It will always compare two signed numbers correctly, REGARDLESS of the value AX-BX. Even if AX-BX causes overflow, the JL will be correct. This is done by considering the following conditions of the flags.
- JL is true if the condition: S^O (i.e., S xor O) is met. Meaning, that JL is true for two conditions:
  - S=1, O=0: AX-BX was negative; and AX-BX didn't overflow.
    Example (8-bit): (-5) - (2) = (-7).
    Result (-7) has the sign bit set
    Thus (-5) is less than (2).
  - S=0, O=1: Overflow!, Sign bit of the result is wrong!
    Consider the following case:
    - AX was a large negative number (-)
    - BX was a positive number (+).
    - The subtraction of (-) and (+) is the same as the addition of (-) and (-).
    - The result caused negative overflow, and thus couldn't be represented as a signed integer correctly (O=1). The result of AX-BX appears positive (S=0).
      Example (8-bit): (-128) - (1) = (+127)
      Result (+127) overflowed. Answer should have been (-129).
      Result appears positive, but overflow occured.
      Thus (-128) is less than (1).

John Lockwood