8/4/2019 Ix -Combinational Circuits (No Animation)

1/19

COMBINATIONAL CIRCUITS

ECE Department

Faculty of Engineering

University of Santo Tomas

8/4/2019 Ix -Combinational Circuits (No Animation)

2/19

Combinational Circuit

Consists of logic gates whose outputsat any time are determined directlyfrom the present combination of inputs

without regard to previous inputs

8/4/2019 Ix -Combinational Circuits (No Animation)

3/19

1. HALF ADDER

Adds mathematically two bits

A B S Cr

0 00 1

1 0

1 1

Inputs Outputs

0 01

1

0

0

0

1

8/4/2019 Ix -Combinational Circuits (No Animation)

4/19

Half Adder Circuit

A

BS

Cr

8/4/2019 Ix -Combinational Circuits (No Animation)

5/19

2. FULL ADDER

Adds mathematically 3 bits

Inputs Outputs

A B C S Cr

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

0

1

1

0

1

0

0

1

0

0

0

1

0

1

1

1

8/4/2019 Ix -Combinational Circuits (No Animation)

6/19

Full Adder Circuit

BC

A

S

Cr

8/4/2019 Ix -Combinational Circuits (No Animation)

7/19

3. HALF SUBTRACTER

Subtracts two bits

A B D Br

0 00 1

1 0

1 1

Inputs Outputs

0 01

1

0

1

0

0

8/4/2019 Ix -Combinational Circuits (No Animation)

8/19

Half Subtracter Circuit

A

BD

Br

8/4/2019 Ix -Combinational Circuits (No Animation)

9/19

4. FULL SUBTRACTER

Subtracts 3 bits

Inputs Outputs

A B C D Br

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

0

1

1

0

1

0

0

1

0

1

1

1

0

0

0

1

8/4/2019 Ix -Combinational Circuits (No Animation)

10/19

Full Subtracter Circuit

A

BC

D

Br

8/4/2019 Ix -Combinational Circuits (No Animation)

11/19

5. BINARY PARALLELADDER Produces the arithmetic sum of two

binary numbers in parallel

Ex. 1101+ 1011

8/4/2019 Ix -Combinational Circuits (No Animation)

12/19

4-bit Full Adders

FA FA FA FAC1C2C3

C4C5

A1

S1

A2

B2

S2

B1

A3A4

B3B4

S3S4

8/4/2019 Ix -Combinational Circuits (No Animation)

13/19

6. LOOK AHEAD CARRY GENERATOR

Gi = carry generate, produces anoutput carry when both Ai and Bi areonePi = carry propagate, associated with

the propagation of the carry from Ci to

8/4/2019 Ix -Combinational Circuits (No Animation)

14/19

Pi = Ai BiGi = AiBi

Si = Pi CiCi+1 = Gi+PiCi

8/4/2019 Ix -Combinational Circuits (No Animation)

15/19

4-bit full adders with look aheadcarry

C1 C1

A1B1

A2

A3

A4

B2

B3

B4

C2

C3

C4

C5

Look-ahead

carrygenerator

C5

P4

P3

P2

P1

P4

G4

P3

G3

P2

G2

P1

G1S1

S2

S3

S4

8/4/2019 Ix -Combinational Circuits (No Animation)

16/19

7. BCD ADDER

Addition of 2 decimal digits in BCDwith carry from a previous state.

9

+ 9

1

19

8/4/2019 Ix -Combinational Circuits (No Animation)

17/19

Binary Sum BCD Sum

K Z8 Z4 Z2 Z1 C S8 S4 S2 S1

0 0 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 1

0 0 0 1 0 0 0 0 1 0

0 0 0 1 1 0 0 0 1 1

0 0 1 0 0 0 0 1 0 0

0 0 1 0 1 0 0 1 0 1

0 0 1 1 0 0 0 1 1 0

0 0 1 1 1 0 0 1 1 1

0 1 0 0 0 0 1 0 0 0

0 1 0 0 1 0 1 0 0 1

0 1 0 1 0 1 0 0 0 0

0 1 0 1 1 1 0 0 0 1

0 1 1 0 0 1 0 0 1 0

0 1 1 0 1 1 0 0 1 1

0 1 1 1 0 1 0 1 0 0

0 1 1 1 1 1 0 1 0 1

1 0 0 0 0 1 0 1 1 0

1 0 0 0 1 1 0 1 1 1

1 0 0 1 0 1 1 0 0 0

1 0 0 1 1 1 1 0 0 1

8/4/2019 Ix -Combinational Circuits (No Animation)

18/19

0 1 0 1 0 1 0 0 0 0

0 1 0 1 1 1 0 0 0 1

0 1 1 0 0 1 0 0 1 0

0 1 1 0 1 1 0 0 1 1

0 1 1 1 0 1 0 1 0 0

0 1 1 1 1 1 0 1 0 1

1 0 0 0 0 1 0 1 1 0

1 0 0 0 1 1 0 1 1 1

1 0 0 1 0 1 1 0 0 0

1 0 0 1 1 1 1 0 0 1

K Z8 Z4 Z2 Z1 C S8 S4 S2 S1

Binary Sum BCD Sum

When to add 6?

When K = 1Z8Z4 = 1Z8Z2 = 1

8/4/2019 Ix -Combinational Circuits (No Animation)

19/19

Carry in

BCD Adder Circuit

4 bit binary adder

addend augend

4 bit binary adder

K Z8 Z4 Z2 Z1C

0

C S8 S4 S2 S1