Half-open bins make the edge case visible instead of text-only. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
The left edge belongs to code four
Input 4 V maps to code 4 with bin [4, 5) V.
4 V ∈ [ 4 , 5 ) V , c = 4 4\ \text{V}\in [4,5)\ \text{V},\quad c=4 4 V ∈ [ 4 , 5 ) V , c = 4 Half-open ADC edge scan The right edge moves to the next code. input=4 V [4, 5) V code=4
The middle of the bin keeps code four
Input 9/2 V maps to code 4 with bin [4, 5) V.
9 2 V ∈ [ 4 , 5 ) V , c = 4 {9\over 2}\ \text{V}\in [4,5)\ \text{V},\quad c=4 2 9 V ∈ [ 4 , 5 ) V , c = 4 Half-open ADC edge scan The right edge moves to the next code. input=9/2 V [4, 5) V code=4
The old right edge starts the next code
Input 5 V maps to code 5 with bin [5, 6) V.
5 V ∈ [ 5 , 6 ) V , c = 5 5\ \text{V}\in [5,6)\ \text{V},\quad c=5 5 V ∈ [ 5 , 6 ) V , c = 5 Half-open ADC edge scan The right edge moves to the next code. input=5 V [5, 6) V code=5