الدرس 22 · Memory elements and clocks

Counters

لم يُترجم بعد؛ يُعرض باللغة الإنجليزية

A counter is a register plus an adder that adds 1. On every rising clock edge the register saves the adder's answer, so a 4-bit counter goes 0, 1, 2 ... 15 and then wraps to 0. Watch it count in binary, wrap and reset, then compare it with a ripple counter built from toggle flip-flops, and see counters at work as clock dividers, timers and the CPU's program counter.

12 دقيقة11 خطوات6 أسئلةIntermediate

شكل 22 · تفاعلي

جارٍ تحميل الرسم…

أو ← →

اختبر نفسك

6 أسئلة سريعة

اختر إجابة لتعرف السبب. تُحفَظ نتيجتك مع تقدّمك.

01A 4-bit counter shows 1111. What does it show after the next rising clock edge?

1111 + 1 = 10000 needs five bits. The register keeps only four, so the extra 1 is lost and the count wraps to 0000.

02How many different values can an 8-bit counter show before it wraps?

n bits give 2^n values. 2^8 = 256, from 0 to 255.

03In a ripple counter, what clocks the second toggle flip-flop?

Each stage is clocked by the one before it, so each bit runs at half the frequency of the previous bit.

04Why can a ripple counter briefly show a wrong number?

Going from 0111 to 1000 it passes through 0110, 0100 and 0000. A synchronous counter changes all bits on one clock edge.

05What does a CPU's program counter hold?

It counts through instruction addresses one by one; a jump loads a new address instead of adding one.

06A watch crystal ticks 32,768 times a second. It feeds a chain of 15 halving (toggle) stages. How often does the last stage tick?

Each stage halves the frequency. 32,768 = 2^15, so 32,768 ÷ 2^15 = 1 tick per second. This is how counters divide a clock to make timers.

المصطلحات الأساسية

المسرد

Counter: A circuit that steps through numbers in order, usually adding 1 on every clock edge.
Register: A group of flip-flops that share one clock and together hold a binary number.
Clock edge: The instant a clock signal changes; on a rising edge it goes from 0 to 1, and flip-flops copy their input then.
Wrap around: Going back to 0 after the largest value: a 4-bit counter goes from 15 (1111) to 0 (0000).
Reset: An input that forces every flip-flop of a counter to 0.
Toggle (T) flip-flop: A flip-flop that flips its output on every clock edge, so its output has half the clock's frequency.
Ripple counter: A chain of toggle flip-flops where each one is clocked by the one before; changes pass along the chain one stage at a time.
Program counter (PC): The register in a CPU that holds the address of the next instruction to run.

تفاصيل إضافية

الملاحظات والمصادر

A rising clock edge is the instant the clock signal goes from low (0) to high (1). Flip-flops in a register copy their input only at that instant (Harris and Harris, Digital Design and Computer Architecture, sections 3.2 and 5.4.1).
An n-bit binary counter counts 0 to 2^n - 1 and then wraps to 0. In Python the same rule is count = (count + 1) % 16 for four bits.
Real parts: Texas Instruments' SN74HC161 is a 4-bit synchronous binary counter whose clear input works without the clock; the SN74HC393 holds two 4-bit ripple counters built from toggle flip-flops, each clocked by the one before.
The figure slows the ripple down so you can see it. In a 74HC393 each stage adds a delay of roughly 13 nanoseconds (typical), so a 4-bit ripple is wrong for only a few tens of nanoseconds.
Nearly all quartz watches use a 32,768 Hz crystal; 32,768 is 2^15, so a 15-stage binary counter overflows once per second.
In MIPS and RISC-V each instruction is 4 bytes long and memory is numbered in bytes, so the program counter usually adds 4. The figure uses one address per instruction, as many teaching CPUs do.

اختبار يتاح بعد الخطوة الأخيرة.