# Binary, Binary Counters and Decade Counters

### Overview

This lesson considers many different counters and the associated circuits. D-Type flip flops are examined as the building blocks of binary counters and binary is considered as the number system used by these counters. A derivative of the binary counter called a BCD counter is used to count from 0 to 9 in binary and is used to represent the decimal number system. 7 segment displays and their associated decoder circuits are used to display the outputs of counters in human readable form. Finally a decade counter that simply has ten sequential outputs is considered. This lesson has less questions than usual and needs a few more videos adding in the future.

### Learning Objectives

• Understand the binary number system
• Use D-Type flip flops to make a binary counter
• Use logic to rest a binary counter after a particular number of counts
• Appreciate the difference between a binary and binary coded decimal (BCD)
• Use a BCD counter IC
• Implement logic circuits using Load and Reset to make a binary counter that counts between any two values
• Understand the function of a 7- segment display
• Use a display driver to make a BCD counter with a 7-segment display
• Design counters that count from 0 to 9 and from 1 to 6
• Cascade several decimal counters to count in 10s and 100s
• Understand the operation of a decade counter such as the 4017
• Use a decade counter to design a sequencer using combinational logic

### Lesson Content

Reading: Start with an understanding of the binary number system. To understand counters it is necessary to know how the numbers 0 to 9 are represented in binary. There is no video for this page as it quite straight forward.

Reading: Binary counters. Read the first four sections covering 1 bit, 2 bit and 3 bit binary counters.

Video (9 min): A video showing the operation of a binary counter. The video starts with a 2 bit counter followed by a 4 bit counter and then looks at the RESET and LOAD operations.

Reading: The 4510 counter IC is a 4 bit binary counter. Read about the operation of this counter and appreciate the meaning of binary coded decimal.

Reading: It is very useful to be able to display the output from a counter in a more conventional format. Read about how 7 segment displays can be used to represent the number 0 to 9 and also lots of different letters.

Reading: Converting the binary output of a counter to the correct inputs to a 7 segment display is the function of a display decoder. Read about the operation of the 4511 decoder including the ability to store the displayed output.

Reading: The 4026 counter conveniently includes a decoder and can be used to drive a 7 segment display directly. The 4026 does not include the functionality of the 4510 and 4511 combination but is simple to use.

Video (4 min): A short video about the very straight forward 4026 counter.

Reading: Finally read about a different type of counter. The 4017 decade counter has 10 outputs and does not count in binary. The 10 outputs are made HIGH is sequence, one after another. This counter is very useful for making sequences when combined with combinational logic gates.

Video (7 min): A demonstration of the 4017 counter in action.

### Lesson Review

Review your learning by working through the presentations or notes which summarise the website content.

Presentation: Powerpoint download. The binary number system and how it applies to counter circuits.

Presentation: Powerpoint download. All about 1, 2 and 3 bit binary counters and how to RESET to zero and LOAD a starting value.

Presentation: Powerpoint download. All the different uses for a 7 segment display including numbers and a range of letters.

Notes: PDF download. 7 segment displays used to represent numbers and letters.

### Self Assessment

Complete either the questions (pdf download) OR the on-line quiz. They are the same questions.

Quiz: Quiz about binary and decimal number systems.

### Self Evaluation

I can:

• Convert decimal number to binary
• Convert binary numbers to decimal
• Describe the operation of a D-Type flip flop configured as a divide by two circuit
• Draw a circuit diagram of a 4 bit binary counter made from D-Type flip flops
• Appreciate that a 4 bit binary counter counts from 0 to 15 in binary
• Recognise the MSB and the LSB for the 4 bit output of a binary counter
• Use combinational logic and the RESET inputs of the D-Type flip flops to reset the output of a binary counter at any given value
• Use combinational logic and the SET inputs of the D-Type flip flops to restart the count at a value other than zero
• Use combinational logic to make a binary counters that counts from 0 to 9 (decimal) and from 1 to 6 (dice)
• Understand the meaning of Binary Coded Decimal
• Design circuits using a BCD counter IC including the LOAD and RESET operations
• Recall the operation of a 7 segment display and appreciate the range of possible numbers and letters that can be displayed
• Appreciate the 7 segment displays may need current limiting resistors or transducer drivers to function correctly
• Appreciate the need for a display driver to convert binary into the required output for a 7 segment display
• Recognise that a display drive is just a complex combinational logic circuit
• Use a decoder IC including the use of the STORE operation
• Design a circuit using a BCD counter, a display driver and a 7 segment display to make a counter that counts from 0 to 9
• Appreciate that a specialist IC can combine a BCD counter and display driver in one package but this has less functionality than using individual ICs
• Cascade several counters to make a counters with displays representing 10s and 100s
• Explain the difference between a BCD counter and a decade counter that has 10 separate outputs
• Understand that for a decade counter with ten outputs, only one output is HIGH at any given moment
• Use a decade counter such as the 4017 IC with combinational logic to make sequences of pulses