Why does this 7-Segment Display not function properly?
The 74LS47 shows the following:
$$
\begin{array}{ccccl}
D &amp; C &amp; B &amp; A \\
0 &amp; 0 &amp; 0 &amp; 0 &amp; \rightarrow 0 \\
0 &amp; 0 &amp; 0 &amp; 1 &amp; \rightarrow 1 \\
0 &amp; 0 &amp; 1 &amp; 0 &amp; \rightarrow 2 \\
0 &amp; 0 &amp; 1 &amp; 1 &amp; \rightarrow 3 \\
0 &amp; 1 &amp; 0 &amp; 0 &amp; \rightarrow 4 \\
0 &amp; 1 &amp; 0 &amp; 1 &amp; \rightarrow 5 \\
0 &amp; 1 &amp; 1 &amp; 0 &amp; \rightarrow 6 \\
0 &amp; 1 &amp; 1 &amp; 1 &amp; \rightarrow 7 \\
1 &amp; 0 &amp; 0 &amp; 0 &amp; \rightarrow 8 \\
1 &amp; 0 &amp; 0 &amp; 1 &amp; \rightarrow 9 \\
1 &amp; 0 &amp; 1 &amp; 0 &amp; \rightarrow c \\
1 &amp; 0 &amp; 1 &amp; 1 &amp; \rightarrow ɔ \\
1 &amp; 1 &amp; 0 &amp; 0 &amp; \rightarrow u \\
1 &amp; 1 &amp; 0 &amp; 1 &amp; \rightarrow 3~horizontal~lines \\
1 &amp; 1 &amp; 1 &amp; 0 &amp; \rightarrow broken~6 \\
1 &amp; 1 &amp; 1 &amp; 1 &amp; \rightarrow 
\end{array}
$$

You show:

$$
\begin{array}{ccccl}
D &amp; C &amp; B &amp; A \\
0 &amp; 0 &amp; 0 &amp; 0 &amp; \rightarrow 2 \\
0 &amp; 0 &amp; 0 &amp; 1 &amp; \rightarrow 3 \\
0 &amp; 0 &amp; 1 &amp; 0 &amp; \rightarrow 2 \\
0 &amp; 0 &amp; 1 &amp; 1 &amp; \rightarrow 3 \\
0 &amp; 1 &amp; 0 &amp; 0 &amp; \rightarrow b \\
0 &amp; 1 &amp; 0 &amp; 1 &amp; \rightarrow 7 \\
0 &amp; 1 &amp; 1 &amp; 0 &amp; \rightarrow b \\
0 &amp; 1 &amp; 1 &amp; 1 &amp; \rightarrow 7 \\
1 &amp; 0 &amp; 0 &amp; 0 &amp; \rightarrow c \\
1 &amp; 0 &amp; 0 &amp; 1 &amp; \rightarrow ɔ
\end{array}
$$

This makes me think your B term is hard-coded to a 1 and that you are misinterpreting a 6 as a b.

Check your B term going into the 74LS47. If it is working, then I think your 74LS47 has a damaged B input.

EDIT: Good to hear that you got it working!