1. Combinational Circuit – Arithmetic Circuit
Parallel Adder
Example: 4-bit adder

2. Combinational Circuit – Arithmetic Circuit
Usage: Poling system (for 6 person)
Use full adder and parallel adder 4-bit (binary)
Each full adder can add 3 polls

3. Combinational Gates – Arithmetic Circuit
Comparator
Magnitude comparator: compare two value A and B to ensure if A>B, A=B or A<B
Classical method need 22n line in TT
Explore dissimilarity
How we compare two 4-bit value A(a3 a2 a1 a0) and B(b3 b2 b1 b0)
If (a3>b3) therefore A>B
If (a3<b3) therefore A<B
If (a3=b3) therefore A=B and so on..

4. Combinational Gates – Arithmetic Circuit
A3’B3 A3 x3
A3 B3’ B3
A3’B3 + x3A2’B2 + x3x2A1’B1 + x3x2x1A0’B0 A2 x2 B2
(A<B) A1 x1
A3B3’ + x3A2B2’ + x3x2A1B1’ + x3x2x1A0B0’ B1 A0 x0
(A>B) B0
(A=B)
x3x2x1x0

5. Combinational Circuit - Arithmetic Circuit
Comparator

6. Combinational Circuit – MSI Circuit
There are four useful MSI circuit
Decoder
Demultiplexer
Encoder
Multiplexer
Block Diagram

7. Combinational Circuit – MSI Circuit
DECODER
Codes used for representing entity, e.g. your name is a code which represent yourself (entity)
This code can be identified (or decoded) using a decoder: Provide code, identify entity
Change binary information from n input line (maximum value for) 2n output line
Is known as line decoder n to m, or n:m or nxm decoder (m<=2n)
Might be used to generate 2n (or less) minterm for n input variable

8. Combinational Circuit – MSI Circuit
DECODER
Example: if code 00, 0, 10, 11is used to identify four bulbs, therefore we need 2-bit decoder
This is 2x4 decoder which select output line based on the given 2 bit.
Truth table

9. Combinational Circuit – MSI Circuit
DECODER
From the truth table, decoder circuit 2x4 is
Notes: each output in 2 variable minterm expression (X’Y’, X’Y, XY’, XY)

10. Combinational Circuit – MSI Circuit
DECODER
Design of 3x8 decoder
Usage? Conversion from binary to octal

11. Combinational Circuit – MSI Circuit
DECODER
In general: for n-bit code, decoder suppose to select up to 2n line

12. Combinational Circuit – MSI Circuit
DECODER – Function execution
Example: Full Adder

13. Combinational Circuit – MSI Circuit
DECODER with Enable
Most decoder has an enable signal, therefore it only active when enable, E=1
Truth table

14. Combinational Circuit – MSI Circuit
DECODER with Enable
In MSI, enable signal for decoder is zero enable, E’, therefore this device only active when enable E’=0

15. Combinational Circuit – MSI Circuit
LARGE DECODER
Large decoder can be built using small size decoder
E.g. 3:8 decoder can be built using 2:4 (with 1 enable) as the following

16. Combinational Circuit – MSI Circuit
LARGE DECODER
E.g. 4:16 decoder can be built using two 3:8 decoder (with 1 enable) as the following.
How can you build 4:16 decoder by using 2:4 decoder with enable?

17. Combinational Circuit – MSI Circuit
ENCODER
Encoder is the inversion of decoder.
Several sets of input line, select one, it produce similar code for selected line
Consist of 2n (or less) input line and n output line
Created from OR gate
Example:

18. Combinational Circuit – MSI Circuit
Truth table