Lesson 2. The counter: six flip-flops count to 63

After this lesson six lamps count in binary — 0, 1, 2 … 63 and around again — and a display shows the same number in decimal. The counter is the heart of the raster scan: in the next lesson two of them visit every dot of the screen.

2.1. The idea: add 1 in a column

On every clock edge the counter adds 1. We know how to add 1 in a column: the lowest digit always flips, the next one when the lowest was 1, and so on.

• XOR with the carry flips a digit: t(i) = Q(i) ⊕ c(i);
• AND passes the carry on: c(i+1) = c(i) · Q(i);
• the carry into the very lowest digit is EN: with EN = 0 counting stops.

Reset. Right after power-up the flip-flops are in an unpredictable state. RST = 1 for one clock edge writes 0 into every digit — real circuits reset this way at power-up. In real chips the reset is usually active-low (/MR on the 74HC161 counter, /RES on the 6502 processor), with one inverter for the whole board; here, for simplicity, it is RST = 1.

2.2. Building

The same project. Delete the lesson 1 setup (switches D, CLK, the DFF chip on the canvas, the lamp); keep Power/Ground.

The idea. The counter adds 1 on every clock edge — and we know how to add 1 in a column: the lowest digit always flips, the next one when the lowest was 1, and so on. XOR with the carry flips a digit, AND passes the carry on: c(i+1) = c(i) · Q(i). The carry into the very lowest digit is EN: EN = 0 — counting stops.

Reset. Right after power-up the flip-flops are in an unpredictable state. To start from zero, RST = 1 for one clock edge writes 0 into every digit — real circuits reset this way at power-up.

Step 1. CNT6 — six digits

Ctrl+G → name CNT6. Chip pins: inputs CLK, EN, RST; outputs Q0–Q5, CO.

CO is lit when the counter has reached 63 and counting is enabled: it is the carry into the next counter — in lesson 3 the row and column counters of the screen connect this way.

Step 2. Canvas: clock, switches, counter, lamps, display

Put the lamps in a row from Q5 on the left to Q0 on the right — that way they read as a binary number. A click on the Clock body changes its frequency: 1Hz, 2Hz, 10Hz, 60Hz and the fast ones.

2.3. Check

If the lamps do not go out after RST, check the AND (reset) gates: each has nRST on its second pin, and the NOT is on RST.

Lesson 2 paste (Cmd+I)

Needs NOT, XOR, AND and DFF from lesson 1.

# Lesson 2 — the 6-bit counter CNT6 with enable, reset and carry.chip CNT6 {  portIn(CLK)  portIn(EN)  portIn(RST)  portOut(Q0)  portOut(Q1)  portOut(Q2)  portOut(Q3)  portOut(Q4)  portOut(Q5)  portOut(CO)  NOT(RST, nRST)  XOR(Q0, EN, t0)  AND(t0, nRST, d0)  AND(EN, Q0, c1)  DFF(D=d0, CLK=CLK, Q=Q0)  XOR(Q1, c1, t1)  AND(t1, nRST, d1)  AND(c1, Q1, c2)  DFF(D=d1, CLK=CLK, Q=Q1)  XOR(Q2, c2, t2)  AND(t2, nRST, d2)  AND(c2, Q2, c3)  DFF(D=d2, CLK=CLK, Q=Q2)  XOR(Q3, c3, t3)  AND(t3, nRST, d3)  AND(c3, Q3, c4)  DFF(D=d3, CLK=CLK, Q=Q3)  XOR(Q4, c4, t4)  AND(t4, nRST, d4)  AND(c4, Q4, c5)  DFF(D=d4, CLK=CLK, Q=Q4)  XOR(Q5, c5, t5)  AND(t5, nRST, d5)  AND(c5, Q5, CO)  DFF(D=d5, CLK=CLK, Q=Q5)} clock{rt=2}(CLK)input(EN)input(RST)CNT6(CLK=CLK, EN=EN, RST=RST, Q0=Q0, Q1=Q1, Q2=Q2, Q3=Q3, Q4=Q4, Q5=Q5, CO=CO)led(Q0)led(Q1)led(Q2)led(Q3)led(Q4)led(Q5)led(CO)