Here is one of the definitions of binary from the Merriam-Webster:
relating to, being, or belonging to a system of numbers having 2 as its base <the binary digits 0 and 1>; involving a choice or condition of two alternatives (as on-off or yes-no)
So binary is a choice between all on or all off. It's either 1 or 0. There's no in-between state. How does this relate to the Gospel?
As I was reflecting on Romans 6, it dawned on me that the Gospel could be described as binary. Consider the tail end of Romans 6:14—"you are not under law but under grace". Paul reminds us that we are under grace. That is, we are saved 100% by what Jesus did on the cross. We contributed nothing toward our salvation. Zero percent.
There are those in Paul's time—as there are in ours—who think that they can contribute something toward their salvation. They are trying to keep the law in order to attain righteousness. Paul calls them "under law". In his day, they would insist on doing parts of the law like circumcision. In our day, such people may insist on a sinner saying the Sinner's Prayer, or that going to church, or that regular tithing, etc., makes one acceptable in God's sight. They are under law.
Such thinking is wrong. Either we rely on Jesus 100% for our salvation, or we do not. We cannot think that we can contribute 1% towards our righteousness through right living or Bible reading or service to the poor. Christ either saves us completely by his effort, or he is not our saviour at all. 1% of our effort plus 99% of Christ's work on the cross does not equal salvation. It equals death. Paul makes this point very clear in Galatians 5:2–3—"If you accept circumcision, Christ will be of no advantage to you. I testify again to every man who accepts circumcision that he is obligated to keep the whole law." In other words, if you want to contribute to your own salvation, Christ's work on the cross is meaningless to you and instead, you must try to keep every letter of the law. Either God does all the work in saving us and giving us righteousness or he does nothing for us.
Hence my thought that the Gospel is binary. Jesus does it all (1) or he does nothing at all (0). It's all Jesus or nothing. Paul unequivocally states that believers of Christ Jesus are under grace, not law. Obeying the law has no part in our salvation because if we want to be under law, we must obey all of the law perfectly. And we know no one is capable of that. As James 2:10 says, "For whoever keeps the whole law but fails in one point has become accountable for all of it." (Italics mine.) And again from Paul in Romans 3:23—"all have sinned and fall short of the glory of God". So there is no one who is capable of keeping the whole law. It is death to be under law. It is life to be under grace. Jesus does all the work in saving us (grace) or he does nothing for us at all (law). Ergo, the Gospel is binary.