1. Basic terminology associated with counter and sequential circuits.
Counters
Basic terminology associated with counter and sequential circuits.
©Paul Godin
Updated Aug 2013

2. Introduction Counters are part of a family called Sequential Circuits.
Sequential circuits provide predictable output patterns.
Sequential circuits are used in many applications, including:
digital counting
counting up or down
arithmetic operations
control circuits
frequency dividers
clocks
timing circuits...

3. Introduction
Basically, counters are devices that are able to count clock pulses.
Counters are constructed from Flip-Flops
Available as counter ICs
Sn74LS192
Up/Down 4-bit counter with preset and clear

4. Digit Significance 10110 MSB LSB
Most Significant Bit (MSB): This bit represents the greatest numerical value, and is the left-most bit in a binary number.
Least Significant Bit (LSB): This bit represents the smallest numerical value, and is the right-most bit in a binary number.
Example:
10110
MSB
LSB

5. Modulus
The Modulus of a counter refers to the number of unique output states it can produce. Also referred to as “MOD”.
Example:
a counter counts in the following sequence: 000, 001, 010, 011, then back to 000
The modulus of this counter is 4. It has 4 unique output states (including zero).

6. Maximum Modulus
The maximum modulus of a counter is 2N, where ‘2’ indicates the number of possible bit states (1 or 0), and ‘N’ represents the maximum number of bits.
The maximum modulus of a 3-bit counter is 8. There are 8 unique output states (from 000 to 111).
What is the maximum modulus of a 5 bit counter?

7. Counter Sequences
A Bit is a single binary digit (1 or 0). A binary number is comprised of multiple bits.
Full Sequence Count refers to a natural count that includes all possible binary numbers. It’s modulus is the same as its maximum modulus.
A Truncated Sequence Count is when the modulus is less than its maximum, or where less than all possible binary numbers are used.

8. Sequential Circuit
Counter states are sequential. An output state will follow another in a sequence.
State Diagrams are used to visually represent the sequence of these states.
000
001
010
011
100
State Diagram of a truncated sequence

9. Sequential Circuits
Counters normally recycle or restart their sequence.
Example:
000
001
010
011
100
101
110
111

10. Up/Down UP DOWN A natural count can be Up or Down: 000 001 010 011 100
101
110
111 UP
DOWN

11. Returns to the first state.
State Table
A State Table is another means of presenting state sequences.
As with the state diagram, the state table determines the next output based on the present output state.
Current
Next QC QB QA 1
Returns to the first state.
State Table

12. Review Questions
A truncated mod-6 3-bit up counter has a starting point of all low outputs.
Draw the state diagram
Draw the state table
If a full sequence down counter has a current output of 0101, what is the next output?
If a counter requires a modulus of 130, what is the minimum number of bits required?

13. Review Questions
What is the modulus of a 4 bit full sequence down counter?
Draw the timing diagram for the following state diagram:
000
001
010
011
100

14. End
©Paul R. Godin
gmail.com