Abstract interpretation is widely used to determine programs’ numerical properties. However, current abstract domains primarily focus on mathematical semantics, which do not fully capture the complexities of real-world programs relying on machine integer semantics and involving extensive bit-vector operations. This paper presents a solution that combines a bit-level abstraction and a word-level abstraction to capture machine integer semantics. First, we generalize the bit-level abstraction used in the Linux eBPF verifier for determining known and unknown bits of real-world programs, by supplementing all required operations as a standard abstract domain. Based on this abstraction, we design an abstract domain that is signedness-aware and simultaneously retains both the above bit-level and the world-level bound information. These two levels of information cooperate via a standard reduced product operation to improve analysis precision. We implement the proposed domains in the Crab analyzer and the out-of-kernel eBPF verifier PREVAL. Experiments demonstrate their effectiveness in analyzing SV-COMP benchmark programs, assisting hardware designs, and eBPF verification.