RT level combinational blocks

1
RT level combinational blocks
2
Goal

• This lecture presents the set of functional
  blocks that are usually considered to be
  elementary or basic at the RT level.

3
Prerequisites

• Lecture 3.3

4
Homework

• No particular homework is foreseen

5
Further readings

• Students interested in making a reference to a
  text book on the arguments covered in this
  lecture can refer, for instance, to
• M. Morris Mano, C.R.Kime Logic and Computer
  Design Fundamentals, 2nd edition
  updatedPrentice Hall, Upple Saddle River, NJ
  (USA), 2001, (chapter 3, pp. 111-148 )

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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
7
Adders

• We shall consider
• half adder
• full adder
• adder-subtracter

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Half-Adder

• A half-adder has
• 2 inputs Ai, Bi
• 2 outputs Si and Ci1
• and computes the binary sum of the 2 input bits,
  providing
• the sum Si
• the carry Ci1

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Ai Bi
Ci1 Si

• Si Ai ? Bi
• Ci1 Ai ??Bi

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Full-Adder

• A full-adder has
• 3 inputs Ai, Bi and Ci
• 2 outputs Si and Ci1
• and computes the binary sum of the 3 input bits,
  providing
• the sum Si
• the carry Ci1

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Ai Bi Ci
?
Ci1 Si

• Si Ai ?? Bi ?? Ci
• Ci1 Ai Bi Ai Ci Bi Ci
• Ai Bi ( Ai ?? Bi ) Ci

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Adder-subtracter

• An adder-subtracter is a combinational block
  capable of adding/subtracting two n-bits inputs
  operands, detecting overflow conditions. It has
• 2 n-bits data inputs, both labeled from n-1 to 0
• 1 control input to select one of the two
  operations
• 1 n-bits data output
• 1 control output asserted when an overflow
  condition is occurred.

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Adder-subtracter (contd)
Symbol
ADD/SUB
A(n-1 downto 0)
FUNC(n-1 downto 0)
OVFL
B(n-1 downto 0)
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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
15
Multiplexer

• A multiplexer is a combinational block capable of
  forcing its output to the current value of one
  of its inputs, according to the values of some
  control signals.
• Each input can be either a single wire or a bus.

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Multiplexer

• A multiplexer has
• 2k data inputs, labeled from 2k-1 to 0
• k control inputs
• 1 data output.

It gets the value present on the input labeled 2
i, where i (0 ? i ? k-1) is the binary number
present on the control inputs.
k
2k-1 2k-2 2 1 0
MUX
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Multiplexer (cont'd)
Symbol
OUT
IN(2k-1 downto 0)
SEL(k-1 downto 0)
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Multiplexer (contd)
Symbol
M0(n-1 downto 0)
M1(n-1 downto 0)
M2(n-1 downto 0)
OUT(n-1 downto 0)
M2k-1(n-1 downto 0)
SEL(k-1 downto 0)
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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
20
Decoder

• A decoder k ? 2k has
• 1 n-bit data input
• 2 n outputs, labeled from 0 to 2 n-1
• 1 enable.
• When enabled, just the output labeled 2 j is
  active, where j is the value present on the data
  input.
• When disabled, no output is active.

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Decoder (contd)
Symbol
DOUT(0)
DOUT(1)
DOUT(2)
DIN(n-1 downto 0)
DOUT(2n-1)
ENABLE
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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
23
Priority Encoder

• A priority encoder has
• 2k inputs, labeled from 0 to 2k-1 (each input is
  assigned a fixed priority)
• k outputs
• 1 data valid output
• 1 enable.

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Priority Encoder (contd)

• When enabled
• the outputs get the value j , where j is the
  label of the highest priority asserted input
• the data valid output is asserted.
• When disabled or when no input is asserted
• the data valid output is not asserted.

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Priority Encoder (contd)
Symbol
M0
VALID
M1
M2
CODE(n-1 downto 0)
M2n-1
ENABLE
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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
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Comparator

• A comparator gets 2 n-bit binary numbers
• A(n-1 downto 0)
• B(n-1 downto 0)
• and provides in output the result of the
  comparison between A and B.
• A control input UM/2C specifies whether the
  input operands are unsigned or signed,
  respectively.

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Comparator (contd)
Symbol
AeqB AneB AltB AgtB AleB AgeB
A
A(n-1 downto 0)
B
B(n-1 downto 0)
UM/2C
Sel
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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
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Counter of 1s occurrences

• A counter of 1s occurrences has
• 1 n-bit data input
• 1 m-bit data output, being m ? log2 n ?.
• The device counts the number of occurrences of a
  1 on its inputs and provides it on its outputs.

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Counter of 1s occurrences(contd)
Symbol
1s C
DIN(n-1 downto 0)
DOUT(m-1 downto 0)
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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
33
ROM

• A 2k ? n ROM (Read-Only Memory) has
• k address inputs
• n data outputs
• 2k n-bit internal cells, storing permanent
  values.
• The outputs gets the value stored in the j cell,
  j being the current value present on address
  inputs.

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ROM (contd)
Symbol
D_OUT
DATA(n-1 downto 0)
ADDR
ADDR(2k-1 downto 0)
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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
36
ALU

• An n-bit ALU (Arithmetic Logic Unit) performs
  logic and/or arithmetic operations on 2 n-bit
  operands, under the control of ad-hoc control
  signals.

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ALU (contd)
Symbol
CONTROL
C_IN
A(n-1 downto 0)
FUNC(n-1 downto 0)
B(n-1 downto 0)
STATUS
C_OUT
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Functions implemented by the ALU 181
Input
Functions
S3
S2
S1
S0
arithmetic (M0)
logic (M1)
0
0
0
0
FA minus 1 plus CIN
FA'
0
0
0
1
FAB minus 1 plus CIN
FA' B'
0
0
1
0
FAB' minus 1 plus CIN
FA' B
0
0
1
1
F1111 plus CIN
F 1111
0
1
0
0
FA plus (AB') plus CIN
FA'B'
0
1
0
1
FAB plus (AB') plus CIN
FB'
FA ? B'
0
1
1
0
FA minus B minus 1 plus CIN
0
1
1
1
FAB' plus CIN
FAB'
1
0
0
0
FA plus (AB) plus CIN
FA'B
FA ? B
1
0
0
1
FA plus B plus CIN
1
0
1
0
FAB' plus (AB) plus CIN
FB
1
0
1
1
FAB plus CIN
FAB
1
1
0
0
FA plus A plus CIN
F0000
1
1
0
1
FAB plus A plus CIN
FAB'
1
1
1
0
FAB' plus A plus CIN
FAB
1
1
1
1
FA plus CIN
FA
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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
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Multiplier

• A multiplier has
• 1 n-bits data inputs, labeled from n-1 to 0
• 1 m-bits data inputs, labeled from m-1 to 0
• no control signals
• k-bits data outputs, labeled from k-1 to 0
• and provides in output the results of the product
  between the two input operands.

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Multiplier (contd)
Symbol

A(m-1 downto 0)
MUL_OUT(k-1 downto 0)
B(n-1 downto 0)
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Multiplier (contd)
Symbol

• Signed operands kmn-1
• Unsigned operands kmn

A(m-1 downto 0)
MUL_OUT(k-1 downto 0)
B(n-1 downto 0)
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Elementary functional blocks
Multiplier
Multiplexer
Adder-Subtracter
Decoder
Encoder
ALU
Comparator
ROM
I/O interfaces
1s counter
44
I/O interfaces

• The combinational interfaces for the following
  I/O devices will be presented
• led bar driver
• 7-segments display
• dip-switch
• keypad.

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Led bar interface
LED_BAR interface
DATA(n-1 downto 0)
n
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7-segments display interface
DATA
DISPLAYinterface
4, 7
DOT
ENABLE
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7-segments display interface
a
a
a
b
BI
f
b
b
g
A
c
c
d
d
B
e
e
C
f
f
c
e
D
g
g
DOT
d
ENABLE
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Dip-switch interface
DIP_SWinterface
DATA
n
n
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Keypad interface
KEYPADinterface
DATA
4, 7
DATA_VALID
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