Common Combinational Logic Circuits - Auburn University

Common Combinational Logic Circuits

? Adders

? Subtraction typically via 2s complement addition

? Multiplexers

? N control signals select 1 of up to 2N inputs as output

? Demultiplexers

? N control signals select input to go to 1 of up to 2N outputs

? Decoders

? N inputs produce M outputs (typically M > N)

? Encoders

? N inputs produce M outputs (typically N > M)

? Converter (same as decoder or encoder)

? N inputs produce M outputs (typically N = M)

C. E. Stroud

Combinational Logic Circuits (10/12)

1

More Common Circuits

? Comparators

? Compare two N-bit binary values

? Equal-to or Not-equal-to

? Easiest to design

? Greater-than, Less-than, Greater-than-or-equal-to, etc.

? Require adders

? Parity check/generate circuit

? Calculates even or odd parity over N bits of data ? Checks for good/bad parity (parity errors) on

incoming data

C. E. Stroud

Combinational Logic Circuits (10/12)

2

Adders

? Consider ith column addition of 2 binary numbers (A and B)

? Ai + Bi + Cini = Couti + Sumi

? Derive truth table

? Populate K-maps

? Obtain minimized SOPs

? Draw logic diagram

? Optimize with P&Ts

Truth Table

A B C Co S 000 0 0 001 0 1 010 0 1 011 1 0 100 0 1 101 1 0 110 1 0 111 1 1

BC A 00 01 11 10

00 1 0 1 11 0 1 0

S=A'B'C+A'BC' +AB'C'+ABC =A'(BC)+A(BC) =ABC

BC A 00 01 11 10

00 0 1 0 10 1 1 1

Co=BC+AC+AB

C. E. Stroud

Combinational Logic Circuits (10/12)

3

Adders

A

B

S=ABC

C

Co=BC+ AC+AB

A

Taking advantage of common B product terms between S and Co C we see that we can use the XOR gate for AB to reduce the gate

count

BC A 00 01 11 10

00 0 1 0 10 1 1 1

Co=A'BC+AB'C+AB =C(A'B+AB')+AB =C(AB)+AB

S=ABC

Co=BC+ AC+AB

C. E. Stroud

Combinational Logic Circuits (10/12)

4

Adders

referred to as a full adder

A

B

S=ABC

C

Co=BC+ AC+AB

now we can build an N-bit adder from N full adders

Cin

A0

AS

S0

B0

B FA

C Co

we can let a block represent the full adder

A

B full S adder

Cin Cout

A1

AS

S1

B1

B FA

C Co

AN-1

AS

BN-1

B FA

C Co

SN-1 Cout

C. E. Stroud

Combinational Logic Circuits (10/12)

5

Subtractors

Build an N-bit subtractor from an N-bit adder using 2's complement

?Recall the 2's complement A0

transformation for a

B0

negative number:

1) invert

A1

2) then add 1

B1

here we use Cin

to add a 1

?Therefore, S=A-B

AN-1

?Note that this includes

BN-1

a sign bit (SN-1)

Cin=1

AS

B FA

C Co

AS

B FA

C Co

AS

B FA

C Co

C. E. Stroud

Combinational Logic Circuits (10/12)

S0 S1

SN-1 Cout

6

Multiplexers

? N control signals select 1 of up to 2N inputs as output

? Sometimes called selectors ? We looked at a 2-to-1 MUX

A

S B

G=4 GIO=11 Gdel=3

C. E. Stroud

A

Z

0Z B

1

Z = AS' + BS S if S=0, then Z=A else if S=1, then Z=B

Combinational Logic Circuits (10/12)

In0

Out In2N-1

N Select Control

7

Short-hand Truth Table

Multiplexers S1 S0 Z

? 4-to-1 MUX

? 4 inputs

? In0-3

? 2 controls

? S1, S0 (LSB)

In0 0 In1 1 In2 2 In3 3

Z

In0

? 1 output

?Z

S1

S1 S0

S0

In1

? Can generated any size MUX

S1

S0

Z = In0 S1' S0' + In1 S1' S0

In2

+ In2 S1 S0' + In3 S1 S0 S0

S1 S0 S0

SOP obtained directly from S1 short-hand Truth Table

S1 In3 S1 S0

0 0 In0 0 1 In1 1 0 In2 1 1 In3

Z

G=7 GIO=25 Gdel=3

C. E. Stroud

Combinational Logic Circuits (10/12)

8

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download