In global navigation satellite system (GNSS) receivers, the acquisition process is the first stage of the signal processing module. It consists of assessing the presence of GNSS signals and providing a rough estimation of the incoming signal parameters: the Doppler frequency and the code delay. However, the presence of bit sign transitions affects receiver performance in signal acquisition detection. This article focuses on the bit transition and its impact on the acquisition performance by providing a general mathematical study and an illustration for two GNSS signals: the global positioning system legacy civil signal (GPS L1 C/A) and Galileo E1 open service (OS). This study is applicable to a terrestrial user in a constraint environment. Furthermore, the presented results are mathematical models of the probability of detection in the presence of bit sign transitions (only one potential bit sign transition per integration interval), and potential uncertainties on the Doppler frequency and code delay. These do not result from empirical acquisition of real signals.