Binary Counters

A register that progresses through a predetermined sequence of states upon the application of input pulses is known as a counter. These input pulses can be clock pulses or may originate from an external source, occurring either at uniform intervals of time or at random. Counters are prevalent in almost all equipment that contains digital logic. They serve the purpose of counting the number of occurrences of an event and are instrumental in generating timing signals to control the sequence of operations in digital computers.

Among the various sequences a counter may follow, the straight binary sequence is the simplest and most straightforward. A counter that follows the binary number sequence is referred to as a binary counter. An n-bit binary counter is a register comprising n flip-flops and associated gates that follows a sequence of states according to the binary count of n bits, from 0 to $2^n - 1$. The design of binary counters can be executed using the procedure outlined for sequential circuits. Alternatively, a simpler design procedure can be derived from a direct inspection of the sequence of states that the register must undergo to achieve a straight binary count.

By examining a sequence of binary numbers such as 0000, 0001, 0010, 0011, and so on, we observe that the lower-order bit is complemented after every count. Every other bit is complemented from one count to the next if and only if all its lower-order bits are equal to 1. For instance, the binary count transition from 0111 (7) to 1000 (8) is achieved by:

1. Complementing the low-order bit.
2. Complementing the second-order bit because the first bit of 0111 is 1.
3. Complementing the third-order bit because the first two bits of 0111 are 1's.
4. Complementing the fourth-order bit because the first three bits of 0111 are all 1's.

A counter circuit typically employs flip-flops with complementing capabilities. Both T and JK flip-flops possess this property. A JK flip-flop is complemented if both its J and K inputs are 1 and the clock undergoes a positive transition. The output of the flip-flop remains unchanged if $J = K = 0$. Additionally, the counter may be controlled with an enable input that turns the counter on or off without removing the clock signal from the flip-flops.

Synchronous binary counters exhibit a regular pattern. In a 4-bit binary counter, for example, the clock inputs (C) of all flip-flops receive the common clock signal. If the count enable is 0, all J and K inputs are maintained at 0, and the output of the counter does not change. The first stage $A_0$ is complemented when the counter is enabled and the clock undergoes a positive transition. Each of the other three flip-flops is complemented when all previous least significant flip-flops are equal to 1 and the count is enabled. The chain of AND gates generates the required logic for the J and K inputs. The output carry can be used to extend the counter to more stages, with each stage increment having an additional flip-flop and an AND gate.

Counters with parallel load are very useful in the design of digital computers. In subsequent chapters, these will be referred to as registers with load and increment operations. The increment operation adds one to the content of a register. By enabling the count input during one clock period, the content of the register can be incremented by one.

Key Points

• Counters: Registers that progress through a predetermined sequence of states with input pulses.
• Binary Counter: A counter that follows a binary sequence from 0 to $2^n - 1$ using n flip-flops.
• Flip-Flops: Used in counters for their complementing capabilities; T and JK flip-flops are commonly used.
• Synchronous Counters: Use a common clock signal for all flip-flops and have a regular pattern.
• Enable Input: Controls the counter, allowing it to be turned on or off without removing the clock signal.
• Parallel Load Counters: Useful in digital computers for load and increment operations.

Understanding the operation and design of binary counters is fundamental in digital logic design, as they are crucial components in timing and control circuits within digital systems.