1. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 1 Combinational Circuit – Arithmetic Circuit Parallel Adder Example: 4-bit adder

2. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 2 Combinational Circuit – Arithmetic Circuit Cascading Adder –Cascade four full adder –Classical method: 9 variable input needs 2 9 = 512 line of truth table Cascading method can be expanded to greater number. Example: 16-bit parallel adder

3. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 3 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

4. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 4 Combinational Gates – Arithmetic Circuit Adder-Subtractor –Use two’s complement X-Y=X+(-Y) –Two’s complement for Y = invert each Y bit and add 1

5. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 5 Combinational Gates – Arithmetic Circuit BCD Adder –Classical method needs 29 lines in TT –As a replacement, we use binary adder with a little alteration

6. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 6 Combinational Gates – Arithmetic Circuit BCD Adder Strategy –Use 4-bit parallel adder to ad 2 BCD code –If answer <10, therefore it is correct (just leave it) –If answer ≥10, therefore some calibration is needed to get to correct C, S 8, S 4, S 2 and S 1. Repeat this strategy for other 4-bit parallel adder

7. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 7 Combinational Gates – Arithmetic Circuit When answer <10, therefore total BCD = total Binary, no calibration is needed When answer ≥10, therefore Calibration Total BCD = Total Binary + requirement for calibration C=K+Z 8.Z 4 + Z 8.Z 2

8. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 8 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(a 3 a 2 a 1 a 0 ) and B(b 3 b 2 b 1 b 0 ) –If (a3>b3) therefore A>B –If (a3<b3) therefore A<B –If (a3=b3) therefore A=B and so on..

9. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 9 Combinational Gates – Arithmetic Circuit A3A3 A2A2 A1A1 A0A0 B2B2 B1B1 B0B0 B3B3 x3x3 x2x2 x1x1 x0x0 A 3 B 3 ’ A 3 ’B 3 (A<B) (A>B) (A=B) A 3 ’B 3 + x 3 A 2 ’B 2 + x 3 x 2 A 1 ’B 1 + x 3 x 2 x 1 A 0 ’B 0 A 3 B 3 ’ + x 3 A 2 B 2 ’ + x 3 x 2 A 1 B 1 ’ + x 3 x 2 x 1 A 0 B 0 ’ x3x2x1x0x3x2x1x0

10. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 10 Combinational Circuit - Arithmetic Circuit Comparator

11. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 11 Combinational Circuit – MSI Circuit There are four useful MSI circuit –Decoder –Demultiplexer –Encoder –Multiplexer Block Diagram

12. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 12 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) 2 n output line Is known as line decoder n to m, or n:m or nxm decoder (m<=2 n ) Might be used to generate 2 n (or less) minterm for n input variable

13. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 13 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

14. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 14 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)

15. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 15 Combinational Circuit – MSI Circuit DECODER Design of 3x8 decoder Usage? Conversion from binary to octal

16. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 16 Combinational Circuit – MSI Circuit DECODER In general: for n-bit code, decoder suppose to select up to 2 n line

17. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 17 Combinational Circuit – MSI Circuit DECODER – Function execution Boolean function in SOM for can be executed with decoder (to generate minterm) and OR gate (used for forming “sum”) Any combinational circuit with n input and m output can be done with n:2 n decoder and with m OR gate Good for circuit with a lot of output, and each function is express with several minterm

18. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 18 Combinational Circuit – MSI Circuit DECODER – Function execution Example: Full Adder

19. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 19 Combinational Circuit – MSI Circuit DECODER with Enable Most decoder has an enable signal, therefore it only active when enable, E=1 Truth table

20. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 20 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

21. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 21 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

22. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 22 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?

23. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 23 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 2 n (or less) input line and n output line Created from OR gate Example:

24. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 24 Combinational Circuit – MSI Circuit Truth table