How to count to 25 cents with coins of 5, 10 and 25 cents. The circuit is constructed using FFs and OR, AND gates.
\documentclass[border=3mm]{standalone}
% Tikz
\usepackage{tikz}
\usetikzlibrary{arrows,shapes.gates.logic.US,shapes.gates.logic.IEC,calc}
% Notation
\usepackage{amsmath, siunitx}
% Tikz Library
\usetikzlibrary{calc}
\tikzset{every picture/.style={line width=0.3mm}}
% Circuitikz
\usepackage[european,straightvoltages,americanresistor]{circuitikz}
\ctikzset{logic ports=ieee}
% Custom
\tikzset{sr-ff/.style={flipflop, flipflop def={t1=S, t3=R, t6=Q}}}
\begin{document}
\tikzstyle{branch}=[fill, shape=circle, minimum size=3pt, inner sep=0pt]
\begin{circuitikz}[line cap=round, line join =round]
% First State
\node[sr-ff] (q0) at (0,0) {};
% Cents
\node[circle, draw, shift={(0,10)}] (5cents) at (q0) {5 cents};
\draw[red] (5cents) -- ++(0,-7.8) coordinate (5cents_line) to[short,-*] +(44.7,0);
\node[circle, draw, shift={(2,0)}] (10cents) at (5cents) {10 cents};
\draw[blue] (10cents) -- ++(0,-5.2) coordinate (10cents_line) to[short,-*] +(42.7,0);
\node[circle, draw, shift={(2,0)}] (25cents) at (10cents) {25 cents};
\draw[orange] (25cents) -- ++(0,-3.6) coordinate (25cents_line) to[short,-*] +(40.7,0);
% Q0 State
\draw (q0.pin 1) -- +(-1,0) node [left] {\texttt{1}}
(q0.pin 6) -- ++(1,0) node[and port, anchor=in 2] (and_q0) {}
($(and_q0.in 1|-5cents_line)$) to[short, *-] (and_q0.in 1);
\node[or port, rotate=180, number inputs=3, shift={(0,10)}] (or_q0_reset) at (q0) {};
\draw (or_q0_reset.out) -- ($(q0.pin 3|-or_q0_reset.out)$) -- (q0.pin 3);
% Q1 State
\draw (and_q0.out) -- ($(and_q0.out|-q0.pin 1)$) -- ++(1,0)
node[sr-ff, anchor=pin 1] (q1) {}
(q1.pin 6) to[short] ($(q1.pin 6|-or_q0_reset.in 3)$) to[short, *-] (or_q0_reset.in 3);
\draw (q1.pin 6) -- ++(1,0) node[and port, anchor=in 2] (and_q1_5) {}
($(and_q1_5.in 1|-5cents_line)$) to[short] (and_q1_5.in 1)
%
(q0.pin 6) to[short, *-] ($(5cents_line-|q0.pin 6) + (0,0.5)$)
coordinate (q0_line) to[short,*-] ($(and_q1_5.in 1|-q0_line)$)
node[and port, anchor=in 2] (and_q1_10) {}
%
($(and_q1_10.in 1|-10cents_line)$) to[short, *-] (and_q1_10.in 1)
(and_q1_5.out) -- ++(1,0) node[or port, anchor=in 2] (or_q1) {}
(and_q1_10.out) -| (or_q1.in 1);
\node[or port, rotate=180, shift={(0,8)}] (or_q1_reset) at (q1) {};
\draw (or_q1_reset.out) -- ($(q1.pin 3|-or_q1_reset.out)$) -- (q1.pin 3);
% Q2 State
\draw (or_q1.out) -- ($(or_q1.out|-q1.pin 1)$) -- ++(1,0)
node[sr-ff, anchor=pin 1] (q2) {}
(q2.pin 6) to[short, *-] ($(q2.pin 6|-or_q1_reset.in 2)$) to[short, *-] (or_q1_reset.in 2)
(q2.pin 6) |- (or_q0_reset.in 2);
\draw (q2.pin 6) -- ++(1,0) node[and port, anchor=in 2] (and_q2_5) {}
($(and_q2_5.in 1|-5cents_line)$) to[short, *-] (and_q2_5.in 1)
%
(q1.pin 6) to[short, *-] ($(5cents_line-|q1.pin 6) + (0,1.5)$)
coordinate (q0_line) to ($(and_q2_5.in 1|-q0_line)$)
node[and port, anchor=in 2] (and_q2_10) {}
%
($(and_q2_10.in 1|-10cents_line)$) to[short, *-] (and_q2_10.in 1)
(and_q2_5.out) -- ++(1,0) node[or port, anchor=in 2] (or_q2) {}
(and_q2_10.out) -| (or_q2.in 1);
\node[or port, rotate=180, shift={(0,6)}] (or_q2_reset) at (q2) {};
\draw (or_q2_reset.out) -- ($(q2.pin 3|-or_q2_reset.out)$) -- (q2.pin 3);
% Q3 State
\draw (or_q2.out) -- ($(or_q2.out|-q2.pin 1)$) -- ++(1,0)
node[sr-ff, anchor=pin 1] (q3) {}
(q3.pin 6) to[short, *-] ($(q3.pin 6|-or_q2_reset.in 2)$) to[short, *-] (or_q2_reset.in 2)
(q3.pin 6) |- (or_q1_reset.in 1);
\draw (q3.pin 6) -- ++(1,0) node[and port, anchor=in 2] (and_q3_5) {}
($(and_q3_5.in 1|-5cents_line)$) to[short, *-] (and_q3_5.in 1)
%
(q2.pin 6) to[short, *-] ($(5cents_line-|q2.pin 6) + (0,0.5)$)
coordinate (q0_line) to ($(and_q3_5.in 1|-q0_line)$)
node[and port, anchor=in 2] (and_q3_10) {}
%
($(and_q3_10.in 1|-10cents_line)$) to[short, *-] (and_q3_10.in 1)
(and_q3_5.out) -- ++(1,0) node[or port, anchor=in 2] (or_q3) {}
(and_q3_10.out) -| (or_q3.in 1);
\node[or port, rotate=180, shift={(0,4)}] (or_q3_reset) at (q3) {};
\draw (or_q3_reset.out) -- ($(q3.pin 3|-or_q3_reset.out)$) -- (q3.pin 3);
% Q4 State
\draw (or_q3.out) -- ($(or_q3.out|-q3.pin 1)$) -- ++(1,0)
node[sr-ff, anchor=pin 1] (q4) {}
(q4.pin 6) to[short, *-] ($(q4.pin 6|-or_q3_reset.in 2)$) to[short, *-] (or_q3_reset.in 2)
(q4.pin 6) |- (or_q2_reset.in 1);
\draw (q4.pin 6) -- ++(1,0) node[and port, anchor=in 2] (and_q4_5) {}
($(and_q4_5.in 1|-5cents_line)$) to[short, *-] (and_q4_5.in 1)
%
(q3.pin 6) to[short, *-] ($(5cents_line-|q3.pin 6) + (0,1.5)$)
coordinate (q0_line) to ($(and_q4_5.in 1|-q0_line)$)
node[and port, anchor=in 2] (and_q4_10) {}
($(and_q4_10.in 1|-10cents_line)$) to[short, *-] (and_q4_10.in 1)
%
(q0.pin 6) to[short, *-] ($(10cents_line-|q0.pin 6) + (0,0.5)$)
coordinate (q1_line) to ($(and_q4_5.in 1|-q1_line)$)
node[and port, anchor=in 2] (and_q4_25) {}
($(and_q4_25.in 1|-25cents_line)$) to[short, *-] (and_q4_25.in 1)
%
(and_q4_5.out) -- ++(1,0) node[or port, anchor=in 3, number inputs=3] (or_q4) {}
(and_q4_10.out) -- ($(and_q4_10.out|-or_q4.in 2)$) -- (or_q4.in 2)
(and_q4_25.out) -- ++(0.6,0) coordinate (and_q4_25_line) --
($(and_q4_25_line|-or_q4.in 1)$) -- (or_q4.in 1);
% Q5 State
\draw (or_q4.out) -- ($(or_q4.out|-q4.pin 1)$) -- ++(1,0)
node[sr-ff, anchor=pin 1] (q5) {}
(q5.pin 6) to[short, -*] ($(q5.pin 6|-or_q3_reset.in 2) + (0,1.5)$) -| (q4.pin 3)
(q5.pin 6) to[short, -*] ($(q5.pin 6|-or_q3_reset.in 1)$) -| (or_q3_reset.in 1)
(q5.pin 6) -- ($(q5.pin 6|-or_q0_reset.in 1)$) to[short] (or_q0_reset.in 1)
(q5.pin 3) -- +(0,-0.4) node[ground] {}
(q5.pin 6) to[short] +(1,0);
% Nodes
\node[circle, draw, fill=black!20] at (q0) {q0};
\node[circle, draw, fill=black!20] at (q1) {q1};
\node[circle, draw, fill=black!20] at (q2) {q2};
\node[circle, draw, fill=black!20] at (q3) {q3};
\node[circle, draw, fill=black!20] at (q4) {q4};
\node[circle, draw, fill=black!20] at (q5) {q5};
\end{circuitikz}
\end{document}