Combinational Circuit – Arithmetic Circuit

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 x3 A3 B3’ A3 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