Ten pins and two commons

Ten legs, and what each one is

Hold the digit with the decimal point at the bottom right. The legs are numbered the way every chip in a two-row package is numbered: from the bottom left, along the bottom, then back along the top from the right.

The row nearest you carries E, D, common, C, H from left to right. The row away from you carries G, F, common, A, B. Two commons, one in the middle of each row, and they are the same connection inside the package.

The order is the same on both parts

Look at the driver board's top row: after VCC and GND, its segment outputs read G F A B. Look at its bottom row: after the three control pins, they read E D C H.

Those are the digit's two rows, in the digit's order. Sit the digit above the board's segment pins and every wire runs down its own column or one hole over.

Four of the eight are directly above their own hole and four shift by one. None of them crosses another, on either row, which gives you a check you can do from across the room: if a jumper crosses another jumper, one of them is wrong.

The two that leave

The commons are the only legs that do not go to the driver board. There is no pin on the board for them — the board drives segments, and the common is the return path for all eight of them together.

They go to a rail instead. GND for a 5161AS, 5 V for a 5161BS, the same rail the board's VCC is on. Getting this wrong is the single most common reason a display that is otherwise wired perfectly stays completely dark, and it looks exactly like a missing ground, so check it first.

One wire is enough electrically. Two is better, because every segment's current comes back through this connection: a digit showing 8. puts eight segments' worth through it, and a breadboard contact is not a great conductor.

Before the wires, the headers

The driver boards arrive with their pin headers loose in the bag. Solder the strip in before the board goes anywhere near a breadboard.

A wire pushed through an unsoldered hole makes a contact that works when you press it and stops when you let go, and whose resistance changes every time anything on the bench moves. The symptom is a segment that comes and goes, or a digit that is right until you touch the board — which reads as a code bug and is not one. The digits themselves need no soldering; their legs are already there.