How do flip-flops count clock pulses in binary and divide a frequency?
Counters: chaining flip-flops to count clock pulses in binary, frequency division by each stage, and the modulus of a counter.
An Eduqas GCSE Electronics answer on counters: how chained flip-flops count clock pulses in binary, how each stage divides the frequency by two, the modulus (number of states) of a counter, and using counters to divide frequency and count events.
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What this dot point is asking
Eduqas wants you to explain how flip-flops are chained to count clock pulses in binary, how each stage divides the frequency by two, and the modulus (number of states) of a counter. Counters are the most common sequential circuit and the bridge from a clock to a useful count or a divided frequency.
The answer
Counting in binary
Frequency division
The modulus of a counter
Uses of counters
Examples in context
Counters are everywhere a digital system needs to keep count or divide time. A digital clock divides a crystal oscillator down to one pulse per second and counts seconds, minutes and hours; a frequency divider produces several timing signals from one clock; a people-counter or a production tally increments on each sensor pulse. The binary count drives a decoder and seven-segment display (the next topic), and the clock that steps the counter is the 555 astable or crystal oscillator from the timing module.
Try this
Q1. State by what factor a single flip-flop divides a frequency. [1 mark]
- Cue. By two (it toggles at half the input rate).
Q2. How many states does a counter of 5 flip-flops have? [1 mark]
- Cue. states (counting to ).
Q3. A clock drives 4 flip-flops in a chain. Find the output frequency of the last stage. [2 marks]
- Cue. .
Exam-style practice questions
Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Eduqas 20194 marksA counter is built from 4 flip-flops. State the maximum number of different states it can have, and explain how this relates to the number of flip-flops.Show worked answer →
Number of states (up to 2 marks): each flip-flop stores one bit (two values), and flip-flops give combinations, so 4 flip-flops give states (counting to ).
Explanation (up to 2 marks): the flip-flops together hold an -bit binary number; with 4 bits the count runs from to , which is different values before it rolls over to again.
Markers reward states and the link to an -bit binary number counting from to .
Eduqas 20224 marksA clock is applied to a chain of 3 flip-flops, each dividing the frequency by two. Calculate the output frequency of the last flip-flop.Show worked answer →
Each flip-flop divides the frequency by two, so a chain of 3 divides by .
Output frequency: .
Markers reward the division by (here ) and the output frequency of . The common error is dividing by (the number of stages) instead of .
Related dot points
- Flip-flops and latches: storing one bit, the difference between sequential and combinational logic, the D-type flip-flop, and edge triggering by a clock.
An Eduqas GCSE Electronics answer on flip-flops and latches: how a flip-flop stores a single bit, the difference between sequential and combinational logic, the D-type flip-flop and how it captures its input on a clock edge, and using flip-flops as memory and to divide frequency.
- Seven-segment displays and decoders: the seven-segment display, the decoder that drives it from a binary count, and common-anode and common-cathode types with current-limiting resistors.
An Eduqas GCSE Electronics answer on seven-segment displays and decoders: how a seven-segment display forms digits, the decoder that converts a binary count into the segment pattern, common-anode and common-cathode types, and the current-limiting resistor each segment needs.
- The 555 astable: producing a continuous square-wave output, the frequency and period equations, the duty cycle, and using an astable as a clock or flasher.
An Eduqas GCSE Electronics answer on the 555 timer in astable mode: how it free-runs to give a continuous square wave, the frequency and period equations, why the standard duty cycle exceeds 50 per cent, and using an astable as a clock, flasher or tone generator.
- Binary numbers and adders: counting in binary, the half adder (sum and carry), the full adder with a carry in, and adding multi-bit numbers.
An Eduqas GCSE Electronics answer on binary arithmetic and adders: counting in binary and converting to decimal, the half adder built from XOR and AND giving sum and carry, the full adder that includes a carry in, and chaining full adders to add multi-bit binary numbers.
Sources & how we know this
- WJEC Eduqas GCSE (9-1) Electronics specification (C490) — WJEC Eduqas (2017)