1. EKT 124 / 3 DIGITAL ELEKTRONIC 1
CHAPTER 2
Digital Combinational
Logic/Arithmetic Circuits

2. Converter
Comparator
Decoder
Encoder
Code Converter

3. Comparator(1)
Compares two binary strings (or binary words) to determine if they are exactly equal.
Truth table for a comparator: A B
A=B 1 A B
A>B
A=B
A<B 1

4. Comparator (2)
The exclusive-NOR gate can be used as basic comparator

5. Comparator – Basic Operation
Example – to compare 2 bit binary number
Compare the 2 LSB (G1) and 2 MSB (G2) of the two number

6. Comparator – 4-bit comparator
Logic symbol for a 4-bit comparator with inequality indication.
Inequality checking
If A3 = 1 and B3=0, A > B
If A3 = 0 and B3=1, A < B
If A3 = B3, examine lower bit
Starting with highest bit order, MSB bit
Highest order indication must take precedence.
To design a comparator to evaluate two 4 bit number
We need 4 X-NORs and 1 4 input AND gates

7. Comparator – 8 bit comparator
For 8 bit magnitude comparator
We use two 4 bit ICs comparator.

8. Decoder - Intro
Digital circuit that detect the presence of specific combination of bits (code) in the input, and indicate the presence of that code in its output.
In digital electronics, a decoder can take the form of a multiple-input, multiple-output logic circuit that converts coded inputs into coded outputs, where the input and output codes are different. e.g. n-to-2n BCD decoders.

9. Decoder- Intro
A decoder is a circuit that creates an output based on the binary states of a given input or it detect the presence of specific combination code

10. Decoder – Basic operation
Let say we want to determine the presence of code bit 1001
We can use AND gate so that it can produce HIGH output by inverting all the 0s inputs
If we use NAND gate – a LOW output will indicate the presence of the code 1001
What is the logic required to decode 1011 by producing HIGH output?

11. Decoder – 4 line to 16 line decoder
Input
A3A2A1A0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

12. Decoder Exmple 3 – 8 Binary decoder

13. Decoder – logic circuit design

14. Example - 7 segment decode
Example: 7 Segment Decoder
A 7 segment decoder has 4-bit BCD input and the seven segment display code as its output.
In minimizing the circuits
for the segment outputs all
non-decimal input combinations
(1010, 1011, 1100,1101, 1110,
1111) are taken as don’t-cares (X)
/Bl D C B A a b c d e f g
0 x x x x
-- don’t care inputs --

15. Decoder – Example Application

16. Encoder
Process of converting familiar symbols or number to a coded format
Encoder converts information such as
decimal number or an alphabetical character into some binary coded form.
Encoder is usually used for:
data representation
data security
data compression

17. Encoder: 8 TO 3 Binary encoder
Example: 8-to-3 Binary Encoder

18. Encoder Exercise Design a Decimal-to-BCD Encoder:
Comes out with a truth table (input/output)
From a truth table, get the equation for each output
Draw a circuit for basic decimal-to-BCD encoder based on output equation.
Note : Do not forgot to label LSB & MSB

19. Encoder – Decimal to BCD
It has 10 inputs 0 – 9, it is 10 input and 4 output decder
Dec Digit A3 A2 A1 A0 1 2 3 4 5 6 7 8 9
Logic symbol for a decimal-to-BCD encoder.

20. Encoder – Decimal to BCD
Bit A3 always high for decimal 8 and 9
Bit A2 always high for decimal 4,5,6 and 7
Bit A1 always high for decimal 2,3,6 and 7
Bit A0 always high for decimal 1,3,5,7 and 9
The circuit diagram for Dec to BCD

21. Code Converter
Device that converts one type of binary representation to another.
Example : BCD to binary and binary to Gray code.
Binary code vs. Gray Code.
To convert binary to Gray code or Gray code to binary, we use X-OR gates. How???

22. Example 1 – BCD to binary conversion
Basic conversion
The value or weight of each bit of BCD number representation
for example 87 in BCD is (87)
BCD Bit
BCD Weight
MSB (64) 32 16 8 4 2 1 A0 A1 A2 A3 B0 10 B1 20 B2 40 B3 80

23. Example BCD representation
Write binary representation of BCD decimal number (27)
binary

24. Binary to Gray code and Gray code to binary
Exclusive or gate can be used for gray – binary conversion
Gray code is numerical code used in computing in which consecutive integers are represented by binary numbers differing in only one digit.

25. Example Gray code to binary and binary to Gray code conversion