by Zack Butler

Solution: LUMEN

This puzzle depicts a fairly simple digital logic circuit (thus the title, "Logical Digits," which also refers to the fact that the circuit will spit out some useful numbers), obfuscated by substituting the numbers on all of the chips with letters in a one-to-one cipher, as shown:



The circuit itself has a timer chip (the AAA [555] in the upper left), a "7493" counter (that counts 0-7 in binary over and over out its three outputs) and several 7400-series logic gates, with eight outputs labeled D7-D0. As the counter cycles through its counting, the outputs (read as an eight-digit binary number, with D7 the largest digit) will cycle through the numbers 18, 92, 0, 177. The cipher suggests that this should be read as an IP address, and it corresponds to LUMEN.mit.edu.

To come to these conclusions, note that there are a bunch of chips (though oddly-labeled ones) and very few other components. One of the chips (labeled "ENPT") has additional information beyond the four-letter chip designation. The extra letters are in standard position for pin numbers (14 and 8 on top, 1 and 7 on bottom). Assuming that the letters on all the chips are enciphered numbers, this gives O = 1, E = 7, I = 8 and N = 4 (since ON is pin 14). This establishes that these are indeed 7400 series digital logic chips, since all the on-chip designations start with EN.

The ENHN chip can only be a 7404 or 7414 inverter (which behave the same for the purposes of this puzzle, though here it must be the more common 7404 and H = 0 since O = 1). This will be confirmed later by noting which pins are inputs to it, as the layout of an inverter is different from most 7400-series chips. ENHH is therefore decipherable to be a 7400, quad 2-input NAND gate.

The only chip that does not have a EN** designation is the chip in the upper left, which is labeled AAA and has some resistors and capacitors attached to it. This is a typical setup for a 555 timer to act as an oscillator, providing a clock to the rest of the circuit, so A = 5. The clock output must be an input to the ENPT chip, and the very unusual locations of Vcc (power input) and ground indicate that this chip must be a 7493 (so now P = 9 and T = 3). The other lines drawn from the ENPT are therefore the counter outputs (and therefore inputs to the other chips).

Tracing the outputs to inputs of ENSH (known to be 74?0) will show that it has two four-input gates, and therefore is a 7420 (S = 2) dual 4-input NAND gate. ENTS is now deciphered to be a 7432, quad 2-input OR gate, and ENIM (M = 6, the only number left over) a 7486, quad exclusive-or gate.

The logic can now be traced, and with D7 the most significant bit of the output and D0 the least significant (this is a common designation for an 8-bit wide data bus), as the counter counts they will represent the (binary) numbers 18, 92, 0, and 177, over and over in that order.

So this gives the substitution of 0123456789 as HOSTNAMEIP. Using the substitution as a hint, the hostname for the IP is LUMEN (.mit.edu).