Sistem Digitalhttp://www.unhas.ac.id/amil/S1TIF/SD2019/

L5. Combinational Circuits

Amil Ahmad Ilham

Outline• Contents:

Introduction

Number System

Logic Gates

Function Minimization

Combinatorial Circuit

Sequential Circuit

• Slides http://www.unhas.ac.id/amil/S1TIF/SD2019/

• Tools: EWB (Electronics Workbench)

2

Vending Machine Design - 3:Definition of variable used

• Assign input variables:1. A = 1 = Rp. 2.000,- entered.2. B = 1 = Rp. 1.000,- entered.3. C = 1 = Rp. 500,- entered.4. D = 1 = Tea requested.5. E = 1 = Coffee requested.6. F = 1 = Milk requested.

• Assign output functions and costs:1. Tea = 1 = Tea dispatched if enough money inserted (Rp. 1.500,-) and Tea is

requested.2. Coffee = 1 = Coffee dispatched if enough money is inserted (Rp. 2.500,-) and

Coffee is requested.3. Milk = 1 = Milk dispatched if enough money is inserted (Rp. 3.000,-) and Milk is

requested.

Vending Machine Design - 3:Truth Table - 1

Tea: Rp. 1.500, Coffee: Rp. 2.500, Milk: Rp. 3.000

Vending Machine Design - 3:Decisions

• Need to decide what to do if: Say, Rp. 2.500,- is tendered, and

Tea and coffee are requested.

• Should you give:• Lowest priced item?

• Highest priced item?

• No item?

• This is decided by carefully considering where to put “1” in the function output columns.

Vending Machine Design - 3:Decisions

• I have decided to dispense a product if only one is selected in order to avoid ambiguity.

• If two products are selected, then no product is dispensed.

• You could make other choices, giving different operation and required different logic.

Vending Machine Design - 3:

Tea: Rp. 1.500, Coffee: Rp. 2.500, Milk: Rp. 3.000

Tea =

Coffee =

Milk =

Output:

A'BCD+AB'C'D+AB'DE'+ADE'F'

AB'CD'E+ABD'EF'

ABD'E'F

Implementation using 16-to-1 Multiplexer (74150)

Strobe S = G’

Output Tea

• Tea = A'BCD+AB'C'D+AB'DE'+ADE'F'

MUX Input DCBA

Non MUXinputs

A’BCD E7 = 1

AB’C’D E9 = 1

AB’C’D E’ = E9

AB’CD E’ = E11

AB’C’D E’F’ = E9

AB’CD E’F’ = E11

ABC’D E’F’ = E13

ABCD E’F’ = E15

Output Tea

• Tea = A'BCD+AB'C'D+AB'DE'+ADE'F'

MUX Input DCBA

Non MUXinputs

A’BCD E7 = 1

AB’C’D E9 = 1

AB’C’D E’ = E9

AB’CD E’ = E11

AB’C’D E’F’ = E9

AB’CD E’F’ = E11

ABC’D E’F’ = E13

ABCD E’F’ = E15

E7 = 1E9 = 1 + E’ + E’F’ = 1E11 = E’ + E’F’E13 = E15 = E’F’E0 =E1=E2=E3=E4=E5=E6=E8=E10=E12=E14 = 0

Output Coffee

• Coffee = AB'CD'E+ABD'EF'

MUX Input DCBA

Non MUXinputs

AB'CD' E = E10

ABC’D' EF’ = E12

ABCD’ EF’ = E14

E10 = EE12 = E14 = EF’E yang lain = 0

Output Coffee

• Coffee = AB'CD'E+ABD'EF'

MUX Input DCBA

Non MUXinputs

AB'CD' E = E10

ABC’D' EF’ = E12

ABCD’ EF’ = E14

E10 = EE12 = E14 = EF’E yang lain = 0

Output Milk

• Milk = ABD'E'F

MUX Input DCBA

Non MUXinputs

ABC’D' E‘F = E12

ABCD' E’F = E14

E12 = E14 = E’FE yang lain = 0

Output Milk

• Milk = ABD'E'FMUX Input DCBA

Non MUXinputs

ABC’D' E‘F = E12

ABCD' E’F = E14

E12 = E14 = E’FE yang lain = 0

Vending Machine Controller

Excexcise - 2Decisions

• Make the machine be able to give change! The machine can dispense Rp. 2.000.-, Rp. 1.000,- and Rp. 500,- coins as a

change.

Only one coin of each denomination is given as change.

Implement it using 16-to-1 Multiplexer (74150)