Unit 4 dica

1
Chapter 4 Combinational Logic
 Logic circuits for digital systems may be
combinational or sequential.
 A combinational circuit consists of input variables,
logic gates, and output variables.

Combinational Logic Design
 It is a process with 5 steps :
2
 Specification
 Formulation
 Optimization
 Technology mapping
 Verification

3
4-2. Analysis procedure
 To obtain the output Boolean functions from a
logic diagram, proceed as follows:
1. Label all gate outputs that are a function of input variables
with arbitrary symbols. Determine the Boolean functions
for each gate output.
2. Label the gates that are a function of input variables and
previously labeled gates with other arbitrary symbols. Find
the Boolean functions for these gates.

4
4-2. Analysis procedure
3. Repeat the process outlined in step 2 until the outputs of
the circuit are obtained.
4. By repeated substitution of previously defined functions,
obtain the output Boolean functions in terms of input
variables.

5
Example
F2 = AB + AC + BC; T1 = A + B + C; T2 = ABC; T3 = F2’T1;
F1 = T3 + T2
F1 = T3 + T2 = F2’T1 + ABC = A’BC’ + A’B’C + AB’C’ + ABC

6
Derive truth table from logic
diagram
 We can derive the truth table in Table 4-1 by using
the circuit of Fig.4-2.

7
4-3. Design procedure
1. Table4-2 is a Code-Conversion example, first, we
can list the relation of the BCD and Excess-3
codes in the truth table.

8
Karnaugh map
2. For each symbol of the Excess-3 code, we use 1’s
to draw the map for simplifying Boolean function.

9
Circuit implementation
z = D’;y = CD + C’D’ = CD + (C + D)’
x = B’C + B’D + BC’D’ = B’(C + D) + B(C + D)’
w = A + BC + BD = A + B(C + D)

10
4-4. Binary Adder-Subtractor
 A combinational circuit that performs the addition of two bits
is called a half adder.
 The truth table for the half adder is listed below:
S = x’y + xy’
C = xy
S: Sum
C: Carry

11
Implementation of Half-Adder

12
Full-Adder
 One that performs the addition of three bits(two
significant bits and a previous carry) is a full adder.

13
Simplified Expressions
S = x’y’z + x’yz’ + xy’z’ + xyz
C = xy + xz + yz
C

14
Full adder implemented in
SOP

15
Another implementation
 Full-adder can also implemented with two half
adders and one OR gate (Carry Look-Ahead
adder).
S = z ⊕ (x ⊕ y)
= z’(xy’ + x’y) + z(xy’ + x’y)’
= xy’z’ + x’yz’ + xyz + x’y’z
C = z(xy’ + x’y) + xy = xy’z + x’yz + xy

16
Binary adder
 This is also called
Ripple Carry
Adder ,because of
the construction with
full adders are
connected in
cascade.

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Carry Propagation (Carry Look
Ahead)
 Fig.4-9 causes a unstable factor on carry bit, and produces
a longest propagation delay.
 The signal from Ci to the output carry Ci+1, propagates
through an AND and OR gates, so, for an n-bit RCA, there
are 2n gate levels for the carry to propagate from input to
output.

18
Carry Propagation (Carry Look
Ahead)
 Because the propagation delay will affect the output signals
on different time, so the signals are given enough time to get
the precise and stable outputs.
 The most widely used technique employs the principle of
carry look-ahead to improve the speed of the algorithm.
Pi : carry propagate (0,1 & 1,0)
Gi : carry generate (0,0 & 1,1)

19
Boolean functions
Pi = Ai ⊕ Bi
Gi = AiBi
Output sum and carry
Si = Pi ⊕ Ci
Ci+1 = Gi + PiCi
Gi : carry generate ;
Pi : carry propagate
when i=0, C1 = G0 + P0C0 --------- (1)
when i=1, C2 = G1 + P1C1 = G1 + P1G0 + P1P0C0 according to (1) -------- (2)
when i=2, C3 = G2 + P2C2 = G2 + P2G1 + P2P1G0 + P2P1P0C0 according to (2)
 C3 does not have to wait for C2 and C1 to propagate.

20
Logic diagram of
carry look-ahead generator
 C3 is propagated at the same time as C2 and C1.
=G0 + P0C0
G0
P0C0
= G1 + P1G0 +
P1P0C0
G1P1G0
P1P0C0
= G2 + P2G1 + P2P1G0 +
P2P1P0C0
G2
P2G1
P2P1G0
P2P1P0C0

21
4-bit Parallel adder with carry look
ahead
 Delay time of n-bit CLAA = XOR + (AND + OR) + XOR

4 bit parallel adder using IC 74182
22

n-Bit Parallel Subtractor
23
 In general subtraction, we made as A-B. Means A+(-B). We can write it
as 2’s Complement of B is added to the A.
 2’s complement means 1’s complement + 1. We make add inverter
across B and take as carry 1. then it will also acts as 2’s complement of B.
 Then we make add that to A, by using adder circuit.

24
Binary subtractor and adder selection in
one design
M = 1subtractor ; M = 0adder
B0 XOR M
(B0 XOR M) + A0 + C0
= 0

Spreadsheet/ Datasheet/
 CARRY LOOK AHEAD 74182.pdf
25

ALU
 A very popular & widely used combinational circuit
is ALU which is capable of performing arithmetic
as well as logical operation.
 Arithmetic Operating Modes:
Addition
Subtraction
Shift Operation
Magnitude Comparison
12 other arithmetic operations
27

 Logical Operating Modes:
Exclusive OR
Comparator
AND, NAND, OR, NOR
10 other arithmetic operations
28

1/8/2012 - L3 Data
Path Design
Copyright 2006 - Joanne
DeGroat, ECE, OSU 29
ALU Operations (integer
ALU)
 Add (A+B)
 Add with Carry (A+B+Cin)
 Subtract (A-B)
 Subtract with Borrow (A-B-Cin)
 [Subract reverse (B-A)]
 [Subract reverse with Borrow (B-A-
Cin)]
 Negative A (-A)
 Negative B (-B)
 Increment A (A+1)
 Increment B (B+1)
 Decrement A (A-1)
 Decrement B (B-1)
 Logical AND
 Logical OR
 Logical XOR
 Not A
 Not B
 A
 B
 Multiply Step or Multiply
 Divide Step or Divide
 Mask
 Conditional AND/OR (uses
Mask)
 Shift
 Zero

ALU Logic Diagram
30
Ao – A3
Bo – B3
Cn Bar
Carry input
So – S3 M
Fo – F3
Cn+4 Bar
A=B
G
P
 it will perform 16 arithmetic & 16 logical operations. Where Ao-A3 & Bo-B3
are the two 4-bit operands. And Cn bar is the carry input with So-S3 are the
select line inputs.
 A special case of M is a mode selection. If M=1 it will performs Logical operations.
if M=0 it will perform Arithmetical Operations.
ALU
74LS181

 ALU IC74181.pdf
 http://www.righto.com/2017/03/inside-
vintage-74181-alu-chip-how-it.html
 ALU IC74F381.pdf
35

36
4-6. Decoders
 The decoder is called n-to-m-line decoder, where
m≤2n
.
 the decoder is also used in conjunction with other
code converters such as a BCD-to-seven_segment
decoder.
 3-to-8 line decoder: For each possible input
combination, there are seven outputs that are equal
to 0 and only one that is equal to 1.

37
Implementation and truth table

3 to 8 Decoder IC 74x138
38
A Y0
74x138
3-to-8 Decoder
B
c
G
1
Y1
Y2
Y3
Y4
Y5
Y6
Y7
G
2
G
3

2 to 4 Decoder using IC 74x139
40
A
Y0
74x139
2-to-4 Decoder
B
1
G
2A
Y1
Y2
Y3
Y0
Y1
Y2
Y3
2
G
2B
Y0
Y1
Y2
Y3

41
INPUT OUTPU
T
G bar B A Y3 bar Y2ba
r
Y1bar Y0bar
1 X X 1 1 1 1
0 0 0 1 1 1 0
0 0 1 1 1 0 1
0 1 0 1 0 1 1
0 1 1 0 1 1 1

42
Decoder with enable input
 Some decoders are constructed with NAND gates, it
becomes more economical to generate the decoder
minterms in their complemented form.
 As indicated by the truth table , only one output can be
equal to 0 at any given time, all other outputs are equal to 1.

SPREADSHEETS
 3 TO 8 LINE DECODER IC74HC
SEREIS.pdf
 IC LV 138 DECODER IC.pdf
 DECODER AND DEMUX IC SPREAD
SHEET.pdf
45

46
Demultiplexer
 A decoder with an enable input is referred to as a
decoder/demultiplexer.
 The truth table of demultiplexer is the same with
decoder.
Demultiplexer
D0
D1
D2
D3
E

47
3-to-8 decoder with enable
implement the 4-to-16 decoder

Cascading binary decoders
(4*16 Decoder using 3*8 decoder )
48
A
B
C
D
ENB
3*8
Decoder
3*8
Decoder
+5v

Example:
 Implement the following multiple output function using 74LS138 and
external gates. F1 (A,B,C)= Σm (1,4,5,7) & F2 (A,B,C)= ∏m (2,3,6,7)
 74LS138 is an 3*8 decoder. The outputs of this ic have active Low. i.e in
SOP form for F1 using NAND gate and POS function for F2 using AND
gate.
49

50
Implementation of a Full Adder
with a Decoder
 From table 4-4, we obtain the functions for the combinational circuit in
sum of minterms:
S(x, y, z) = ∑(1, 2, 4, 7)
C(x, y, z) = ∑(3, 5, 6, 7)

BCD to 7 segment Display Encoder
51
Inputs Outputs
Digit
A B C D a b c d e f g
0 0 0 0 0 1 1 1 1 1 1 0
1 0 0 0 1 0 1 1 0 0 0 0
2 0 0 1 0 1 1 0 1 1 0 1
3 0 0 1 1 1 1 1 1 0 0 1
4 0 1 0 0 0 1 1 0 0 1 1
5 0 1 0 1 1 0 1 1 0 1 1
6 0 1 1 0 1 0 1 1 1 1 1
7 0 1 1 1 1 1 1 0 0 0 0
8 1 0 0 0 1 1 1 1 1 1 1
9 1 0 0 1 1 1 1 1 0 1 1

Display Decoder
52
BCD.xls
IC 7447

4-9. Encoders
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 One of the main disadvantages of standard digital encoders is that they can
generate the wrong output code when there is more than one input present at
logic level “1”. For example, if we make inputs D1 and D2 HIGH at logic “1” both
at the same time, the resulting output is neither at “01” or at “10” but will be at
“11” which is an output binary number that is different to the actual input
present.

55
 Priority encoders output the highest order input first for example, if input
lines “D2“, “D3” and “D5” are applied simultaneously the output code would be
for input “D5” (“101”) as this has the highest order out of the 3 inputs. Once
input “D5” had been removed the next highest output code would be for input
“D3” (“011”), and so on.

56
 An encoder is the inverse operation of a decoder.
 We can derive the Boolean functions by table 4-7
z = D1 + D3 + D5 + D7
y = D2 + D3 + D6 + D7
x = D4 + D5 + D6 + D7

Encoder
An implementation
x=D4+D5+D6+D7
y=D2+D3+D6+D7
z=D1+D3+D5+D7
 limitations
 illegal input: e.g. D3=D6=1
 the output = 111 (¹3 and ¹6)
57Mr. M.PAVAN KUMAR DICA ECE Department
RIT

58
Priority encoder
 If two inputs are active simultaneously, the output
produces an undefined combination. We can establish an
input priority to ensure that only one input is encoded.
 Another ambiguity in the octal-to-binary encoder is that an
output with all 0’s is generated when all the inputs are 0; the
output is the same as when D0 is equal to 1.
 The discrepancy tables on Table 4-7 and Table 4-8 can
resolve aforesaid condition by providing one more output to
indicate that at least one input is equal to 1.

59
Priority encoder
V=0no valid inputs
V=1valid inputs
X’s in output columns represent
don’t-care conditions
X’s in the input columns are
useful for representing a truth
table in condensed form.
Instead of listing all 16
minterms of four variables.

Priority Encoder
 Resolve the ambiguity of illegal inputs
 Only one of the input is encoded
 D3 has the highest priority
the lowest priority D0 has
 X: don't-care conditions
 V: valid output indicator
RIT

Priority Encoder
1
RIT

Priority Encoder
x = D2 + D3
y = D3 + D1D2′
V = D0 + D1 + D2 + D3
RIT

63
IC 74LS 348 8 TO 3 PRIORITY ENCODER
A
74LS 348
8-to-3 Priority encoder
B
c
E1
E0
G
S
Y0
Y1
Y2
Y3
Y4
Y5
Y6
Y7

Multiplexer
Select binary information from one of many input
lines and direct it to a single output linen
2 input lines, n selection lines and one output line
E.g.: 2-to-1-line multiplexer
Two-to-one-line multiplexer
RIT

4-to-1-Line Multiplexer
RIT

67
8 to 1 Multiplexer using IC 74LS 151
74LS 151
8 to 1 mux
Io
I1
I2
I3
I4
I5
I6
I7
EN
So S1 S2
Z
Zbar

68
 For Dual 4 to 1 Multiplexer we are using IC 74LS153. it has two set of input
4 Lines and with two set of Enables with two set of output lines.
 For 16 to 1 Multiplexer we are using IC 74LS150. It has 16 input lines with
4 Select lines along with one Enable Active low and one output

Boolean Function
Implementation Using MUX
MUX: a decoder + an OR gate
2 -to-1 MUX can implement any Boolean function of n
input variable.
Procedure:
 assign an ordering sequence of the input variable
 the rightmost variable (D) will be used for the input lines
 assign the remaining n-1 variables to the selection lines w.r.t.
their corresponding sequence
 construct the truth table
n
 consider a pair of consecutive
 determine the input lines
minterms starting from m0
RIT

70
BOOLEAN FUNCTION IMPLEMENTATION USING MULTIPLEXERS

Boolean Function
Implementation Using MUX
Example: Given F(x,y,z)= Σ(1,2,6,7) implement mux using
RIT
4 × 1 MUX

85
Boolean function implementation
 A more efficient method for implementing a Boolean function
of n variables with a multiplexer that has n-1 selection
inputs.
F(x, y, z) = Σ(1,2,6,7)

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Three-State Gates
 A multiplexer can be constructed with three-state gates.

Four-to-One-Line Multiplexer
RIT`

88
Three state gates
Gates statement: gate name(output, input, control)
>> bufif1(OUT, A, control);
A = OUT when control = 1, OUT = z when control = 0;
>> notif0(Y, B, enable);
Y = B’ when enable = 0, Y = z when enable = 1;

89
2-to-1 multiplexer
 HDL uses the keyword tri to
indicate that the output has
multiple drivers.
module muxtri (A, B, select, OUT);
input A,B,select;
output OUT;
tri OUT;
bufif1 (OUT,A,select);
bufif0 (OUT,B,select);
endmodule

Parity Circuits
 Parity Generator and Checker:
 A parity generator is a combinational logic circuit that generates
the parity bit in the transmitter. On the other hand, a circuit that checks
the parity in the receiver is called parity checker. A combined
circuit or devices of parity generators and parity checkers are commonly
used in digital systems to detect the single bit errors in the transmitted
data word.
 The sum of the data bits and parity bits can be even or odd . In even
parity, the added parity bit will make the total number of 1s an even
amount whereas in odd parity the added parity bit will make the total
number of 1s odd amount.
 Such error detecting and correction can be implemented by using Ex-
OR gates (since Ex-OR gate produce zero output when there are even
number of inputs).
90

Parity Generator
 It is combinational circuit that accepts an n-1 bit stream data and
generates the additional bit that is to be transmitted with the bit stream.
This additional or extra bit is termed as a parity bit.
Parity generators
Even Parity Odd Parity
 In even parity bit scheme, the parity bit is ‘0’ if there are even
number of 1s in the data stream and the parity bit is ‘1’ if there
are odd number of 1s in the data stream.
 In odd parity bit scheme, the parity bit is ‘1’ if there are even number
of 1s in the data stream and the parity bit is ‘0’ if there are odd
number of 1s in the data stream.
91

Even Parity Generator
 a 3-bit message is to be transmitted with an even parity bit. Let the three
inputs A, B and C are applied to the circuits and output bit is the parity
bit P. The total number of 1s must be even, to generate the even parity
bit P.
92

Odd Parity Generator
 the 3-bit data is to be transmitted with an odd parity bit. The three inputs
are A, B and C and P is the output parity bit. The total number of bits
must be odd in order to generate the odd parity bit.
94

Parity Checker
 It is a logic circuit that checks for possible errors in the transmission.
This circuit can be an even parity checker or odd parity checker
depending on the type of parity generated at the transmission end.
When this circuit is used as even parity checker, the number of input bits
must always be even.
 Consider that three input message along with even parity bit is
generated at the transmitting end. These 4 bits are applied as input to
the parity checker circuit which checks the possibility of error on the
data. Since the data is transmitted with even parity, four bits received at
circuit must have an even number of 1s.
 If any error occurs, the received message consists of odd number of 1s.
The output of the parity checker is denoted by PEC (parity error check).
96

Even Parity Checker
 The below table shows the truth table for the even parity checker in
which PEC = 1 if the error occurs, i.e., the four bits received have odd
number of 1s and PEC = 0 if no error occurs, i.e., if the 4-bit message
has even number of 1s.
97

Odd Parity Checker
 The below figure shows the truth table for odd parity generator where PEC =1 if
the 4-bit message received consists of even number of 1s (hence the error
occurred) and PEC= 0 if the message contains odd number of 1s (that
means no error).
99

Parity Generator/Checker IC 74180
 It is a 9-bit parity generator or checker used to detect errors in high
speed data transmission or data retrieval systems. The figure below
shows the pin diagram of 74180 IC
 This IC can be used to generate a 9-bit odd or even parity code or it can
be used to check for odd or even parity in a 9-bit code (8 data bits and
one parity bit).
101

Comparators
 Data comparison is needed in digital systems while performing
arithmetic or logical operations.
 This comparison determines whether one number is greater than, equal,
or less than the other number.
 A digital comparator is widely used in combinational system and is
specially designed to compare the relative magnitudes of binary
numbers.
 These are also available in IC form with different bit comparing
configurations such as 4-bit, 8-bit, etc.
 Whenever we want to compare the two binary numbers, first we have to
compare the most significant bits (MSB).
 If these MSBs are equal, then only we need to compare the next
significant bits. But if the MSBs are not equal, then it would be clear that
either A is greater than or less than B and the process of comparison
ceases.
102

Comparators
Identity Comparators: Comparators that have only one output terminal and produces
the output either low or high are identity comparators.
Magnitude Comparators: Comparators with three output terminals and checks for
three conditions i.e greater than or less than or equal to is magnitude
comparator.
103
Identity Magnitude

 Digital Comparators :
104
 These comparators can compare 2-bit, 4-bit and 8-bit numbers depending on the
application requirement. These are available in TTL as well as CMOS logic family ICs
and some of these ICs include IC 7485 (4-bit comparator), IC 4585 (4-bit comparator in
CMOS family) and IC 74AS885 (8-bit comparator).

 Single Bit Magnitude Comparator :
A comparator used to compare two bits,
i.e., two numbers each of single bit is called a single bit comparator.
 This comparator compares the two bits and produces one of the 3
outputs as L (A<B), E (A=B) and G (A>B).
105

 2 Bit Magnitude Comparator : A 2-bit comparator compares two binary
numbers, each of two bits and produces their relation such as one
number is equal or greater than or less than the other.
107

4 Bit Comparator
 It can be used to compare two four-bit words. The two 4-bit numbers are
A = A3 A2 A1 A0 and B3 B2 B1 B0 where A3 and B3 are the most
significant bits.
 It compares each of these bits in one number with bits in that of other
number and produces one of the following outputs as A = B, A < B and
A>B. The output logic statements of this converter are
 If A3 = 1 and B3 = 0, then A is greater than B (A>B). Or
 If A3 = B3, and if A2 = 1 and B2 = 0, then A > B. Or
 If A3 = B3, & A2 = B2, and if A1 = 1, and B1 = 0, then A>B. Or
 If A3 = B3, A2 = B2, and A1 = B1, and if A0 = 1 and B0=0, then A>B.
 Then we can write logical expression for (A>B) as
110

 The equal output is produced when all the individual bits of one number
are exactly coincides with corresponding bits of another number. Then
the logical expression for A=B output can be written as
E = (A3 Ex-NOR B3) (A2 Ex-NOR B2) (A1 Ex-NOR B1) (A0 Ex-NOR B0)
 In this the four outputs from Ex-NOR gates are applied to AND gate to
give the binary variable E or A = B. The other two outputs are also use
Ex-NOR outputs to generate the Boolean functions as shown figure.
111

4 bit Comparator IC 7485
 This IC can be used to compare two 4-bit binary words by grounding I
(A>B), I (A<B) and I (A=B) connector inputs to Vcc terminal. The figure
below shows the pin diagram of IC7485.

113

8 Bit Comparators using IC7485
 An 8-bit comparator compares the two 8-bit numbers by cascading of
two 4-bit comparators. The circuit connection of this comparator is
shown below in which the lower order comparator A<B, A=B and A>B
outputs are connected to the respective cascade inputs of the higher
order comparator.
114

Barrel Shifter
 A barrel shifter is a digital circuit that can shift a data word by a
specified number of bits without the use of any sequential logic, only
pure combinational logic.
 A barrel shifter is often used to shift and rotate n-bits in modern
microprocessors, typically within a single clock cycle.
 One way to implement it is as a sequence of multiplexers where the
output of one multiplexer is connected to the input of the next multiplexer
in a way that depends on the shift distance.
 By using 4 to 1 multiplexer we are designing 4 bit shiffter. We required 4,
4 to 1 multiplexers along with connection wires.
115

4 bit Barrel Shifter
W(0) W(1) W(2) W(3)
W(3) W(0) W(1) W(2)
W(2) W(3) W(0) W(1)
W(1) W(2) W(3) W(0)
4 * 1
MUX (1)
4 * 1
MUX(2)
4 * 1
MUX(3)
4 * 1
MUX(4)
Y(0) Y(1) Y(2) Y(3)

Truth Table of 4 bit Barrel Shifter :
117
Select
Lines
4 *1 mux (1) 4 *1 mux (2) 4 *1 mux (3) 4 *1 mux (4)
S1 S0 I0 I1 I2 I3 I0 I1 I2 I3 I0 I1 I2 I3 I0 I1 I2 I3
0 0 w(0)
- - - w(1)
- - - w(2)
- - - w(3)
- - -
0 1 - w(3)
- - - w(0)
- - - w(1)
- - - w(2)
- -
1 0 - - w(2)
- - - w(3)
- - - w(0)
- - - w(1)
-
1 1 - - - w(1)
- - - w(2)
- - - w(3)
- - - w(0)
Select Lines output
S1 S0 Y(0) Y(1) Y(2) Y(3)
0 0 W(0) W(1) W(2) W(3)
0 1 W(3) W(0) W(1) W(2)
1 0 W(2) W(3) W(0) W(1)
1 1 W(1) W(2) W(3) W(0)

 VHDL code for 4 bit Barrel Shifter:
library IEEE;
use ieee std_logic_all;
use ieee numeric_std.all;
entity 4bitbs is
port (w: in unsigned (3 down to 0);
S : in unsigned (1 down to 0);
Y : out unsigned (3 down to 0));
end 4bitbs;
Architecture beh of 4bitbs is
begin
Process (S,w)
118
case S is
when “00” => Y <= w ;
when “01” => Y <= w ROR1 ;
when “10” => Y <= w ROR2 ;
when others => Y <= w ROR3 ;
end case;
end process;
end beh ;

Floating point encoder
 Simple Floating point encoder which has encoding of 11 bit fixed point
number into a 7-bit floating point number.
11-Bit fixed point 7-Bit Floating point number
119
4-Bit Mantissa + 3-Bit Exponent
 In this format it have the range between
We have the relation between fixed point number to floating point number
B = M * 2^ E + T

 Representation of fixed point number to floating point number :
120
B10 B9 B8 B7 B6 B5 B4 B3 B2 B
1
B
0
1 0 1 1 1 0 1 0 0 1 0
M3 M2 M1 M0
1 0 1 1
E2 E1 E0
1 1 1
Truncation
Error
1010010
1490 = 11 * 2^7 + 84
B10 B9 B8 B7 B6 B5 B4 B3 B2 B
1
B
0
0 0 1 0 1 0 0 0 1 0 0
M3 M2 M1 M0
1 0 1 0
E2 E1 E0
1 0 1
Truncation
Error
00100
324 = 10 * 2^5 + 4

121
B10 B9 B8 B7 B6 B5 B4 B3 B2 B
1
B
0
0 0 0 0 0 0 1 1 1 0 0
M3 M2 M1 M0
1 1 1 0
E2 E1 E0
0 0 1
Truncation
Error
0
28 = 14 * 2^1 + 0
B10 B9 B8 B7 B6 B5 B4 B3 B2 B
1
B
0
0 0 0 0 0 0 0 0 1 0 0
M3 M2 M1 M0
0 1 0 0
E2 E1 E0
0 0 0
Truncation
Error
0
4 = 4 * 2^0 + 0

ALL IC’s in Combinational Design
 Binary parallel Adder: IC74LS83/IC74LS283
 Carry Look Ahead Adder: IC74182
 ALU : IC 74LS181 (for LSI) / IC74×381 & 382 (for MSI)
 Decoder: 3 to 8 => IC74×138
2 to 4 => IC74×139
7 segment Display => IC7447
 Encoder 8 to 3 Priority : IC74LS348/148

124

 Qud 2 input Mux: IC74×157
 Dual 1 to 4 Demux : IC74×154
 PARITY Generator/Checker : IC74180/280
 Comparators: 4 bit => IC7485
8 bit => IC74×682
 Multiplexer : 4×1 => IC74LS153

8×1 => IC74LS151

16×1 => IC74LS150
125

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