Digital Electronics Page

Gray Codes

This is a technique where we convert number from binary to grays. We do this because Gray reduces the bits we need to change to get to the next number. e.g. changing from 2 to 3 decimal requires a 1 bit change.

Decimal	BCD	Gray Code
0	0000	0000
1	0001	0001
2	0010	0011
3	0011	0010
4	0100	0110
5	0101	0111
6	0110	0101
7	0111	0100
8	1000	1100
9	1001	1101
10	1010	1111

Excess-3 Codes

Conversion to Excess-3

To get an excess-3 code of a decimal number simply add 3 to each decimal digit. And then we write the 4-bit binary number for each digit of the decimal number. We can find the excess-3 code of the given binary number by using the following steps:

• We find the decimal number of the given binary number.
• Then we add 3 in each digit of the decimal number.
• Now, we find the binary code of each digit of the newly generated decimal number.

We can also add 0011 in each 4-bit BCD code of the decimal number for getting excess-3 code.

Decimal	BCD	Excess-3
0	0000	0011
1	0001	0100
2	0010	0101
3	0011	0110
4	0100	0111
5	0101	1000
6	0110	1001
7	0111	1010
8	1000	1011
9	1001	1100

For example the excess-3 Code for 25.35 would be

25.35
33 33
-----
58 68

Which is

5 0100
8 1000
6 0110
8 1000

Therefore

01001000.01101000

Addition is Excess-3

Addition in Excess-3 is just binary addition with one more rule If you need to carry a number you need to remove +3, if you don't carry a number you need to subtract 3. i.e. if the addition of a number result in an extra digit (carry) you need to add. An Example

Let's add 27 and 39
Step 1 Calculate Binary for numbers

 27 = 0010 0111
 39 = 0011 1001

Step 2 Calculate Excess-3 for these

 0010 0111     
 0011 0011
 ---------
 0101 1010 <= Excess-3 for 27
 
 0011 1001
 0011 0011
 ---------
 0110 1100 <= Excess-3 for 39

Step 3 Add Excess-3 codes together

 0101 1010
 0110 1100
 ---------
      (carry 1)
 1000 0110

Step 4 Add or take away 3 from each side. In this case we carried on the right so we add and subtract on the left

 1000  0110
-0011 +0011 
 ----------
 1001  1001
    9     9 <- This is the Excess-3 result NOT the answer we need to convert back to BCD to get the answer

Or we can convert the known answer 27 + 39 = 66 to Excess-3

   66      0110 0110   
   33      0011 0011 
 ----      ---- ----
   99      1001 1001

Signed Number

The signed numbers are represented in three ways.

• Sign-Magnitude form

In this form, a binary number has a bit for a sign symbol. 1=negative 0=Positive

• 1's Compliment.E.g 10101110 invert each bit 01010001.This is a positive number
• 2's Compliment. E.g 10101110 invert each bit 01010001 Then add 1 to the LSB of this result 01010001+1=01010010

Digital Logic Gates

This a IC which make decisions based on signals from there inputs. Basic digital logic gates perform logical operations of AND, OR and NOT on binary numbers.
There are commonly two types

• TTL Transitor-Transistor Logic such as 7400 series. They use NPN and PNP type PJTs
• CMOS Complementary Metal-Oxide-Silicon which is the 4000 series. They use MOSFET or JFET type Field Effect Transistors

You can also make these by using Diodes, Transistors and Resistors to produce an RTTL, Resistor, Transistor logic Gate.

Logic States

In digital logic design only two voltage levels or states are allowed and these states are generally referred to as Logic “1” and Logic “0”, or HIGH and LOW, or TRUE and FALSE.
TTL and CMOS have the following Logic Levels

Note

• VCC refers to a common positive supply of bipolar ICs (no doubt related to a collector).
• VDD refers to the common positive supply of CMOS circuits (no doubt related to a drain)

NOT Gate

Truth Table

With each Gate comes a Truth Table. Here is the NOT gate

Circuit

And here it is built as a circuit. If there is a current flow to ground. If not current it flows to Q. Or more professionally put If A is HIGH, the transistor turns on. When the transistor is turned on, Q is pulled LOW through the transistor. If A is LOW, the transistor is off and Q is pulled HIGH through the resistor up to VCC.

ICs

To make life a bit easier we can use integrated circuits for this.

Here is the pinout for a 74LS04

D-Latches

Types

There are two of D Latches

Edge Triggered

For edge triggered D Latches there are two types, rising edge and falling edge. The rising edge stores the value in D at the time the clock rising. The falling edge stores the value in D at the time the clock falls.

Transparent

For transparent D latches there are two types, active high and active low. For active high the value of D is mimicked when the clock is high. The active low mimics the value of D when the clock is low.

Timings

Here are timings showing the different values of Q depending on the type of latch

Event Detection

We can use a rising edge to detect an event. In the diagram below we can set a state using Key A in Q of the D-Latch. Once set we can tie Key B to the clock of the D-Latch. As long as the switch is closed Q remains constant. But if Key B is opened the value of Q changes and remains the same until another reset on Key A changes

D Flip-flop Clock Divider

Using a rising edge flp-flop you can feed the clock into a flip flop.

The output will be half frequency of the input

D Flip-flop Counter

When using a falling edge D flip flop and feeding Q into clock we can create create a timer. The result of adding all of the Q values is 1 more each time

Here is the circuit