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

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

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..

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

Combinational Circuit - Arithmetic Circuit Comparator

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

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

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

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)

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

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

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

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

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

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

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?

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:

Combinational Circuit – MSI Circuit Truth table