Exercise 3.3: Binary Counters

1) Binary Counting: The Theory

We have built a T Flip-Flop that toggles between 0 and 1 every time the clock ticks. This is a 1-bit counter. But to count higher (0, 1, 2, 3...), we need more bits.

Let's look at the pattern of binary numbers:

• 00 (0)
• 01 (1) -> The 1s bit toggles.
• 10 (2) -> The 1s bit toggles back to 0, and the 2s bit toggles to 1.
• 11 (3) -> The 1s bit toggles.

The Golden Rule of Counting: Notice a pattern?

The 1s bit toggles on every clock pulse. The 2s bit only toggles when the 1s bit flips from 1 to 0. The 4s bit only toggles when the 2s bit flips from 1 to 0.

This "1 to 0" transition is a Falling Edge. If we connect the output of one flip-flop to the clock input of the next, we create a chain reaction. This is called an Asynchronous (Ripple) Counter.

[Image of Ripple Counter Timing Diagram]

In a 4-bit ripple counter, if the current count is 0111 (7), what happens on the next clock pulse?

-- 1s bit: 1->0; 2s bit 1->0; 4s bit: 1->0; 8s bit: 0->1 Result: 1000. Only the 1s bit toggles. Result: 0110. All bits reset to 0000. The counter stops.

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2) Designing a 4-Bit Binary Counter

We will build a 4-bit counter using T Flip-Flops. Since we are using 7474 D Flip-Flops, we need to wire them as T Flip-Flops using XOR gates (like we did in the last section).

Why use XOR gates? This gives us a Count Enable switch. If Enable is 0, the XOR gates pass the current value back to D (Hold). If Enable is 1, they pass the inverted value (Toggle).

Hardware Components

• 2x 7474 Dual D Flip-Flop ICs (Total 4 Flip-Flops)
• 1x 7486 Quad XOR Gate IC (Total 4 XOR Gates)
• 1x 74LS48 BCD to 7-Segment Decoder (From Module 1)
• 1x 7-Segment Display (Common Cathode)
• 1x Push Button (Clock)
• 2x 10kΩ Resistors (One for current limiting and other for debouncing)
• 1x 10µF Capacitor (For debouncing)
• 1x Toggle Switch (Enable)

Wiring Strategy

We need 4 bits: Q0 (LSB), Q1, Q2, Q3 (MSB).

1. The Enable Line: Connect your Toggle Switch to one input of all four XOR gates. This is your master "Count / Pause" switch.
2. Bit 0 (Q0):
   • Clock: Connect to your Push Button (Debounced).
   • Feedback: Q0 -> XOR Input A. XOR Output -> D0.
3. Bit 1 (Q1):
   • Clock: Connect to Q0' (Not Q0) of the previous flip-flop.
   • Note: Since 7474 is Rising Edge triggered, using Q' allows it to toggle when Q falls.
   • Feedback: Q1 -> XOR Input A. XOR Output -> D1.
4. Bit 2 (Q2):
   • Clock: Connect to Q1' of the previous flip-flop.
   • Feedback: Q2 -> XOR Input A. XOR Output -> D2.
5. Bit 3 (Q3):
   • Clock: Connect to Q2' of the previous flip-flop.
   • Feedback: Q3 -> XOR Input A. XOR Output -> D3.

If we disconnect the Enable line from the XOR gates and tie that input to Ground (0) instead, what will the counter do when we press the clock button?

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3) Connecting the Display

Counting with LEDs is fun, but reading binary "1011" is slow. Let's visualize it with a 7-segment display!

We will use the 74LS48 Decoder you used in Module 1.

Wiring Steps

1. Place the 74LS48: Straddle the center gap. Power Pin 16 (VCC) and Pin 8 (GND).
2. Connect Inputs:
   • Connect Q0 (from Flip-Flop 1) to Input A (Pin 7) of 74LS48.
   • Connect Q1 (from Flip-Flop 2) to Input B (Pin 1) of 74LS48.
   • Connect Q2 (from Flip-Flop 3) to Input C (Pin 2) of 74LS48.
   • Connect Q3 (from Flip-Flop 4) to Input D (Pin 6) of 74LS48.
3. Connect Display: Wire outputs a-g to your 7-segment display pins (a-g). Don't forget the current limiting resistor on the Common Cathode (GND) pin!

Test It:

• Set Enable to 1.
• Press the Clock button.
• Does it count? 0, 1, 2, 3... 9.

The 74LS48 is a BCD (Binary Coded Decimal) decoder. What happens if we send it the binary number 1111 (Decimal 15)?

-- It displays 'F'. It displays nothing (Blank). It displays a glitchy symbol and not a valid decimal digit. It displays 7.

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Which is the IC that can count and also decode for 7 segment displays with reset at 10?

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4) Making a Decade Counter

The counter we made so far is capable of incrementing count at clock pulse. The counter counts all the way from 0 to 15 in binary. But for our BCD to 7-segment display decoder, we need to input between 0 (0000) and 9 (1001) for it to output valid numbers and avoid glitchy symbols. Refer to the datasheet of 7474 IC, and answer the question below.

According to the 7474 IC datasheet, which pin and logic level must be used to immediately force the output (Q) to 0, completely ignoring the clock signal?

-- Apply a HIGH (1) signal to the CLR (Clear) pin. Apply a LOW (0) signal to the CLR (Clear) pin. Apply a LOW (0) signal to the PRE (Preset) pin. Connect both the D and CLK pins to Ground (0).

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So if we reset the flip-flops once when they reach the count 10, they all reset to 0 and the subsequent clock pulse restarts the count from 0. The following will be the flow of the counter.

Activity: Wiring the Reset Logic

To make our counter stop at 9 and reset, we need to build a circuit that detects the number 10. In binary, 10 is 1010.

• Q3 (8s bit) is 1
• Q2 (4s bit) is 0
• Q1 (2s bit) is 1
• Q0 (1s bit) is 0

Notice that the number 10 is the very first time that both Q3 and Q1 are HIGH at the same time. If we monitor these two pins, we can trigger a reset exactly when the counter hits 10.

Since the CLR pins on our 7474 flip-flops are Active-Low (they need a 0 to reset), we need a gate that outputs a 0 only when both its inputs are 1. The NAND Gate does exactly this!

Components You'll Need

• Your existing 4-bit Binary Counter circuit (from the previous section)
• 1x 7400 Quad 2-Input NAND Gate IC
• Additional jumper wires

Step-by-Step Design

Step 1: Free the Clear Pins In your previous 4-bit counter build, you connected the CLR pins (Pins 1 and 13 on both 7474 ICs) directly to VCC (5V) so they wouldn't reset randomly.

1. Disconnect Pin 1 and Pin 13 on both 7474 chips from the VCC rail.
2. Use jumper wires to connect all four of these CLR pins together into a single "Master Reset" line on your breadboard.

Step 2: Add the NAND Gate IC

1. Place the 7400 IC on your breadboard straddling the center gap.
2. Connect Pin 14 to VCC (5V) and Pin 7 to GND.

Step 3: Wire the Detection Logic We will use the first NAND gate on the 7400 IC (Inputs on Pins 1 & 2, Output on Pin 3).

1. Connect a wire from Q1 (Pin 9 of your first 7474 IC) to Pin 1 of the 7400 IC.
2. Connect a wire from Q3 (Pin 9 of your second 7474 IC) to Pin 2 of the 7400 IC.

Step 4: Trigger the Reset

1. Connect the output of the NAND gate (Pin 3 of the 7400 IC) to your "Master Reset" line (which connects to all four CLR pins on your flip-flops).

Test It Out! Turn on your power and pulse the clock button. Watch your 7-segment display (or LEDs). It should count: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9... and on the next press, immediately snap back to 0! You have successfully built a Decade (Mod-10) Counter.

Why didn't we also need to connect Q2 and Q0 to the NAND gate to detect the number 10 (1010)? Why is monitoring just Q3 and Q1 enough?

-- Because a 2-input NAND gate only has room for two wires. Because 10 is the lowest number in the counting sequence where both the 8s bit and 2s bit are HIGH simultaneously. Because Q2 and Q0 are always 0 during the entire counting sequence. Because the 7-segment decoder ignores Q2 and Q0.

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Which is the IC that can count with clock and also decode for 7 segment displays with reset at 10?

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5) Understanding CD4026 IC

You have built a 4-bit counter from scratch! This is how engineers built computers in the 1960s. However, for our final digital clock, we will have to wire a lot of such flip-flops which can be tedious.

In Module 1, you used the CD4026 Decade Counter.

• The IC has a counter and a BCD to 7 segment display decoder built-in.
• The counter is automatically reset when it hits 10, making sure it only counts from 0-9.
• One IC can count till 9. To add an extra digit, the carry out pin of 1s digit can be connected to the CLK input of another such IC connected to a 7 segment display, which will act as the 10s digit. Same procedure can be used to extend the counter to 100s and so on.

The CD4026 IC is functionally similar to the circuit we made on breadboard so far. It can be used to replace all the gates, flip-flops and wiring we did and to design digital clocks.

Upload a video showing your counter incrementing whenever you pulse the clock pin of the first flip-flop. Count through all the possible values.

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In the next section, we will learn about a different application of D flip flops which is a register file, before heading towards our project of making a Digital Clock.