1. COE 202: Digital Logic Design Combinational Circuits Part 1
Dr. Ahmad Almulhem
ahmadsm AT kfupm
Phone:
Office:
Ahmad Almulhem, KFUPM 2009

2. Objectives Logic Circuits Design Procedure Examples Combinational
Sequential
Design Procedure
Examples
Ahmad Almulhem, KFUPM 2009

3. Introduction Logic circuits have two classes:
Combinational Circuits
Sequential Circuits
Combinational circuits consist of logic gates with inputs and outputs
The outputs at any instance of time depend only on the combination of the input values based on logic operations such as AND, OR etc.
Sequential circuits, in addition to inputs and outputs also have storage elements, therefore the output depends on both the current inputs as well as the stored values
Ahmad Almulhem, KFUPM 2009

4. Combinational Circuits
n inputs
Combinational Circuit
m outputs . .
A Combinational Circuit
A combinational circuit has:
A set of m Boolean inputs,
A set of n Boolean outputs, and
n switching functions, each mapping the 2m input combinations to an output such that the current output depends only on the current input values
Ahmad Almulhem, KFUPM 2009

5. Design Procedure Specification Formulation Optimization
Write a specification for the circuit if one is not already available
Specify/Label input and output
Formulation
Derive a truth table or initial Boolean equations that define the required relationships between the inputs and outputs, if not in the specification
Apply hierarchical design if appropriate
Optimization
Apply 2-level and multiple-level optimization (Boolean Algebra, K-Map, software)
Draw a logic diagram or provide a netlist for the resulting circuit using ANDs, ORs, and inverters
Ahmad Almulhem, KFUPM 2009

6. Design Procedure (Cont.)
Technology Mapping
Map the logic diagram or netlist to the implementation technology selected
Verification
Verify the correctness of the final design manually or using simulation
Ahmad Almulhem, KFUPM 2009

7. Practical Considerations
Cost of gates (Number)
Maximum allowed delay
Fanin/Fanout
Ahmad Almulhem, KFUPM 2009

8. Example 1
Question: Design a circuit that has a 3-bit input and a single output (F) specified as follows:
- F = 0, when the input is less than (5)10
- F = 1, when the input is greater than (5)10
Solution: Step 1: Label the inputs (3 bits) as X, Y, Z
X is the most significant bit, Z is the least significant bit
The output of the circuit is high when input is greater than (101)2. Therefore, output will be logic 1 for the input combinations: (101)2, (110)2, (111)2
The output will be logic 0 for the other inputs
Ahmad Almulhem, KFUPM 2009

9. Example 1 Step 2: Truth table is defined for this function as:Y Z F 1
Step 3: Minimization YZ X
F = XZ + XY 1
Step 4: Circuit Design X Z F X Y
Ahmad Almulhem, KFUPM 2009

10. Example 2: Code Converters
Code converters convert from one code to another. e.g. BCD to Excess-3 code
The inputs are defined by the code that is to be converted BCD for this example (How long is the input?)
The outputs are defined by the converted code. Excess-3 for this example
Design a BCD-to-Excess-3 Code Converter.
Excess-3 code is a decimal digit plus three converted into binary. 0 is 0011, 1 is 0100, etc.
Ahmad Almulhem, KFUPM 2009

11. Example 2: BCD to Excess-3 Converter (Formulation/Truth Table)
BCD Input
Excess 3 Output
Decimal A B C D W X Y Z 1 2 3 4 5 6 7 8 9
10-15
All other inputs
Ahmad Almulhem, KFUPM 2009

12. Example 2: BCD to Excess-3 Converter (Optimization)AB AB 00 01 11 10 00 01 11 10
X X X X
X X
X X X X
X X W X CD CD AB AB 00 01 11 10 00 01 11 10
X X X X
X X
X X X X
X X Z Y
Ahmad Almulhem, KFUPM 2009

13. Example 2: BCD to Excess-3 Converter (Circuit)
W = A + BC + BD
X = B’C + BC’D’+B’D
Y = CD + C’D’
Z = D’
Ahmad Almulhem, KFUPM 2009

14. Example 3: BCD to 7 Segment Display Controller (Description)
This display controller is used in devices such as digital watches to display digits
Each digit consists of 7 segments (C0, C1,…C6)
The segments are Light Emitting Diodes (LEDs), which light up whenever the value of the segment is 1, and are off when the value of the segment is 0
Example: 7 is displayed by setting C0=C1=C2 = 1 C0 C5 C1 C6 C4 C2 C3
Ahmad Almulhem, KFUPM 2009

15. Example 3: BCD to 7 Segment Display Controller (Specification)
Step 1: Specify the inputs and the outputs for the circuit
4 inputs (A, B, C, D)
7 outputs (c0, c1, c2, c3, c4, c5, c6)
Invalid inputs (BCD greater than 1001) will turn off all display LEDs (all zeroes)
Ahmad Almulhem, KFUPM 2009

16. Example 3: BCD to 7 Segment Display Controller (Formulation/Truth Table)
BCD INPUT
7 SEGMENT OUTPUT
Decimal A B C D C0 C1 C2 C3 C4 C5 C6 1 2 3 4 5 6 7 8 9
10-15
All Other Inputs
Ahmad Almulhem, KFUPM 2009

17. Example 3: BCD to 7 Segment Display Controller (Optimization)AB AB 00 01 11 10 00 01 11 10 C1 C0 CD CD AB AB 00 01 11 10 00 01 11 10 C3 C2
Ahmad Almulhem, KFUPM 2009

18. Example 3: BCD to 7 Segment Display Controller (Optimization)AB AB 00 01 11 10 00 01 11 10 C4 C5 CD AB 00 01 11 10 C6
Ahmad Almulhem, KFUPM 2009

19. Example 3: BCD to 7 Segment Display Controller (Optimization)
C0 = A’C + A’BD + AB’C’ + B’C’D’
C1 = A’B’ + A’C’D’ + A’CD + B’C’
C2 = A’B + B’C’ + A’C’ + A’D
C3 = A’CD’ + A’B’C + B’C’D’+AB’C’+A’BC’D
C4 = A’CD’ + B’C’D’
C5 = A’BC’ + A’C’D’ + A’BD’ + AB’C’
C6 = A’CD’ + A’B’C + A’BC’ + AB’C’
Ahmad Almulhem, KFUPM 2009

20. Conclusion There are two types of logic circuits Design Procedure
Combinational
Sequential
Design Procedure
Specification *
Formulation *
Optimization *
Technology Mapping
Verification
Examples
Ahmad Almulhem, KFUPM 2009