On the Subject of Alpha-Bits
Part of a well-balanced breakfast!
This module displays an ID number, six small screens containing single alphanumeric characters, and a large screen that can be controlled by up- and down-arrows.
It takes a maximum of three boolean operations to uniquely determine the values of two ordered bits. Each small screen is associated with a letter (displayed on the screen) and a boolean operation (determined from the ID number). The binary representation of the letter on the screen represents the converted bitwise result of the associated boolean operation being performed on the two unknowns in each stage.
Characters whose binary representations need more than five digits will not appear anywhere on this module. Numbers use standard binary representations. Letters are to be converted to base 36 before being converted to binary; A = 01010, B = 01011, ..., U = 11110, V = 11111.
Truth Tables
Truth tables for each of the 8 bitwise operations that may appear in this module (shown with their ID number equivalents) are shown here. The two left columns are the inputs in order, and the right column is the output.
0: OR | 1: AND | 2: XOR | 3: IMP | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | |||
1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | |||
0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | |||
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
4: NOR | 5: NAND | 6: XNOR | 7: IMPBY | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | |||
1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | |||
0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | |||
0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |