This document provides an overview of combinational circuits including adders, subtractors, and code converters. It discusses the design process for combinational circuits and considerations like minimizing gates and propagation time. Specific circuit components are then explained, including half adders, full adders, half subtractors, and full subtractors. Their truth tables and logic diagrams are presented. Finally, code converters are briefly mentioned as an application of combinational circuits.

1. Unit- 1
Combinational Circuits
(Adders, Subtractors, Code Converters)
Presentation
By
Dr. Kesavan Gopal
Course: CSE211: Computer
Organization and Design

2. Outline
• Designing of Combinational Circuit
• Combinational Circuit Design Procedure
• Practical Design Consideration
• Adders
– Half- Adders - Definition, Procedure
– Full Adders - Definition, Procedure
• Subtractor
– Half- Subtractors - Definition, Procedure
– Full Subtractors - Definition, Procedure
• Code Converters

3. Designing of Combinational Circuit
• Defn: The design of combinational circuits starts
from the verbal outline of the problem and ends in
a logic circuit diagram or a set of Boolean functions
from which the logic diagram can be easily
obtained.

4. Combinational Circuit Design Procedure
1. The problem is stated
2. The number of available input variables and
required output variables is determined.
3. The input and output variables are assigned letter
symbols.
4. The truth table that defines the required
relationships between inputs and outputs is
derived.
5. The simplified Boolean function for each output is
obtained
6. The Logic diagram is drawn.

5. Practical Design Consideration
A practical design method would have to consider
such constraints as:
1. Minimum number of gates
2. Minimum number of inputs to a gate
3. Minimum propagation time of the signal through
the circuit.
4. Minimum number of interconnections
5. Limitations of the driving capabilities of each gate

6. ADDERS
• Digital Computers performs variety of information
processing tasks.
• Addition of two binary digits.
• WKT: Augend, addend, Sum, Carry
• Half-Adder: A combinational circuit that performs
the addition of two bits is called a half-adder.
• Full Adder: A combinational circuit that performs
the addition of three bits is a full-adder.
• Two half adders - to implement a full adder.

7. HALF - ADDERS
Step 1: Two binary inputs and two binary outputs.
Step 2: The two variables designate Augend and
addend bits. The output variables produce the sum
and carry.
Step 3: Two input variables say x & y and two output
variables S (for sum) and C (for carry).
Step 4: Truth table formulation as below.

8. Cont…
Step 5: The simplified SOP expressions are:
S = x’y + xy’
C = x y
Step 6: Logic Diagram – Various implementations of
Half-Adders:

9. Cont…

10. FULL - ADDERS
Step 1: Three binary inputs and two binary outputs.
Step 2: The Three variables designate Augend and
addend bits. The output variables produce the sum
and carry.
Step 3: Three input variables say x, y & z and two
output variables S (for sum) and C (for carry).
Step 4: Truth table formulation as below.

11. Cont…
Step 5: The simplified SOP expressions are:
S = x’y’z +x’yz’ + xy’z’ + xyz
C = x y + xz + yz
Step 6: Logic Diagram – Various implementations of
Full-Adders:

12. Cont…

13. SUBTRACTORs
• Taking the complement of the subtrahend and
adding it to the minuend.
• Full adders are used for implementation

14. HALF- SUBTRACTOR
• Defn: A Half-Subtractor is a combinational circuit that
subtracts two bits and produces their difference. It
also has an output to specify if a 1 has been
borrowed.
• Designate the minuend bit with x and subtrahend bit
by y.
• To perform x - y, we have to check the relative
magnitudes of x and y. the result is called the
difference bit. x<y, we have to 0 - 1 and it is necessary
to borrow a 1 from the next higher stage.
• Symbol: Difference D; Borrow B:
• Truth Table:

15. HALF- SUBTRACTOR
• Boolean function:
• D = x’y + x y’
• B = x’y
• Note: D exactly same as that of the S of half
adder.

16. FULL - SUBTRACTOR
• Defn: A full- subtractor is combinational circuit that
performs a subtraction between two bits, taking
into account that a 1 may have been borrowed by
a lower significant stage.
• Three inputs and two outputs
• The three inputs x,y and z namely the minuend,
subtrahend and previous borrow respectively. The
two output D and B represent the difference and
output borrow.

17. FULL - SUBTRACTOR
• Truth Table:
• Simplified Boolean functions:
D = x'y'z + x'yz’ + xy'z' + xyz
B = x'y + x'z + yz

18. Code- Converters
Application: Combinational Circuit
Examples: BCD to Excess 3 Code converter
Workout

19. References
[1] Digital Logic and Computer Design by Morris
Mano, 2nd Edition.

20. Queries ?