Page 124 - Handout Digital Electronics

LECTURE 16 BINARY COUNTERS
16.1 Introduction

A binary counter is a sequential circuit (device) that can go through a certain predefined number of
states. It can count or down. Counters are used in almost all digital computers. A binary counter can be
constructed from the JK flip flop because of its toggling nature.

Applications

Counters are used to count the number of instructions in programs, for example the program counter
(PC), containing the address of the next instruction to be executed.

Direct counting

Counters are used for direct counting in manufacturing, for example to count the number of products.
They are also used in digital conversions to count the number of sequences. A binary counter can be
used as a frequency divider.

16.2 Counter Types
There are two types of counters namely:

• Asynchronous Up or Down counter
• Synchronous Up or Down counter

An UP counter can count from zero (0) to a predefined number. In general, an Up-counter counts from 0
n
to 2 – 1, where n is the number of flip flops used to implement the counter. For an example if a binary
n
counter is implemented using three (3) flip flops, then it will count from 0 to 7, that is 2 -1. A Down
n
counter will count from a predefined number say 2 to 0, for example if there are four flip flops in the
counter it will count from 15 to 0.

16.3 4 –bit Asynchronous binary up counter
Figure 54 shows the 4-bit asynchronous binary up counter implemented on the T flip flop (the special
JK flip flop where the J and K inputs are combined. This counter operates as follows:
Initially all the inputs, Q0, Q1, Q2, and Q3 are set to zero. The J and K inputs are tied to a high (5 volts),
so they are ready to toggle with the application of each clock pulse. The flip flops used in the above
circuit are triggered by a 1 to 0 clock transition.

When the clock is in a 1 to 0 transition, and J = K = 1, this toggles the present output at Qo to a 1. Since
each flip flop can only store 1 bit, the 1 displaces the zero (0) which is passed on to the clock of FF1,
which remains at state Q1 = 0. So, the situation is Q3 = 0, Q2 = 0, Q1 = 0, Q0 = 1. Counting always
starts with flip flop FF0. So, if the clock pulse is applied to FF0, since J and K are ready to toggle, the
output at Q0 is toggled to 0, the zero (0) displaces the 1 which is passed on to the clock of FF1, this
toggles the output at Q1 from 0 to 1. The one (1) displaces the zero (0) which is passed on to FF2, which
does not change its state since clock (C) = 0. The same applies to FF3. The counter will count from 0
to15 for example:

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