Datasheet MC14560BCL, MC14560BCP, MC14560BD Datasheet (Motorola)

Page 1
MOTOROLA CMOS LOGIC DATA
1
MC14560B
 
The MC14560B adds two 4–bit numbers in NBCD (natural binary coded
decimal) format, resulting in sum and carry outputs in NBCD code.
This device can also subtract when one set of inputs is complemented with
a 9’s Complementer (MC14561B).
significant digit is connected to VSS for no carry in.
Diode Protection on All Inputs
Supply Voltage Range = 3.0 Vdc to 18 Vdc
Capable of Driving Two Low–power TTL Loads or One Low–power
Schottky TTL Load Over the Rated Temperature Range
MAXIMUM RATINGS* (Voltages Referenced to V
SS
)
Symbol
Parameter Value Unit
V
DD
DC Supply Voltage – 0.5 to + 18.0 V
Vin, V
out
Input or Output Voltage (DC or Transient) – 0.5 to VDD + 0.5 V
Iin, I
out
Input or Output Current (DC or Transient), per Pin
± 10 mA
P
D
Power Dissipation, per Package† 500 mW
T
stg
Storage Temperature – 65 to + 150
_
C
T
L
Lead Temperature (8–Second Soldering) 260
_
C
*Maximum Ratings are those values beyond which damage to the device may occur. †Temperature Derating:
Plastic “P and D/DW” Packages: – 7.0 mW/_C From 65_C To 125_C Ceramic “L” Packages: – 12 mW/_C From 100_C To 125_C
TRUTH TABLE*
Input Output
A4 A3 A2 A1 B4 B3 B2 B1 CinC
out
S4 S3 S2 S1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0
0 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1
*Partial truth table to show logic operation for representative input values.
This device contains protection circuitry to guard against damage due to high static voltages or electric fields. However, precautions must be taken to avoid applications of any voltage higher than maximum rated voltages to this high-impedance circuit. For proper operation, Vin and V
out
should be constrained to the range VSS (Vin or V
out
) VDD.
Unused inputs must always be tied to an appropriate logic voltage level (e.g., either VSS or VDD). Unused outputs must be left open.

SEMICONDUCTOR TECHNICAL DATA
Motorola, Inc. 1995
REV 3 1/94

  
Motorola, Inc. 1994
REV 0 1/94

BLOCK DIAGRAM
L SUFFIX
CERAMIC
CASE 620
ORDERING INFORMATION
MC14XXXBCP Plastic MC14XXXBCL Ceramic MC14XXXBD SOIC
TA = – 55° to 125°C for all packages.
P SUFFIX
PLASTIC
CASE 648
D SUFFIX
SOIC
CASE 751B
7 13
15 14
1 2 3 4 5 6
12
11
10
9
C
in
A1 B1
A2 B2 A3 B3 A4 B4
S1
S2
S3
S4
C
out
VDD = PIN 16
VSS = PIN 8
Page 2
MOTOROLA CMOS LOGIC DATAMC14560B
2
ELECTRICAL CHARACTERISTICS (Voltages Referenced to V
SS
)
V
– 55_C 25_C 125_C
Characteristic
Symbol
V
DD
Vdc
Min Max Min Typ # Max Min Max
Unit
Output Voltage “0” Level
Vin = VDD or 0
V
OL
5.0 10 15
— — —
0.05
0.05
0.05
— — —
0 0 0
0.05
0.05
0.05
— — —
0.05
0.05
0.05
Vdc
“1” Level
Vin = 0 or V
DD
V
OH
5.0 10 15
4.95
9.95
14.95
— — —
4.95
9.95
14.95
5.0 10 15
— — —
4.95
9.95
14.95
— — —
Vdc
Input Voltage “0” Level
(VO = 4.5 or 0.5 Vdc) (VO = 9.0 or 1.0 Vdc) (VO = 13.5 or 1.5 Vdc)
V
IL
5.0 10 15
— — —
1.5
3.0
4.0
— — —
2.25
4.50
6.75
1.5
3.0
4.0
— — —
1.5
3.0
4.0
Vdc
“1” Level (VO = 0.5 or 4.5 Vdc) (VO = 1.0 or 9.0 Vdc) (VO = 1.5 or 13.5 Vdc)
V
IH
5.0 10 15
3.5
7.0 11
— — —
3.5
7.0 11
2.75
5.50
8.25
— — —
3.5
7.0 11
— — —
Vdc
Output Drive Current
(VOH = 2.5 Vdc) Source (VOH = 4.6 Vdc) (VOH = 9.5 Vdc) (VOH = 13.5 Vdc)
I
OH
5.0
5.0 10 15
– 3.0
– 0.64
– 1.6 – 4.2
— — — —
– 2.4
– 0.51
– 1.3 – 3.4
– 4.2
– 0.88
– 2.25
– 8.8
— — — —
– 1.7
– 0.36
– 0.9 – 2.4
— — — —
mAdc
(VOL = 0.4 Vdc) Sink (VOL = 0.5 Vdc) (VOL = 1.5 Vdc)
I
OL
5.0 10 15
0.64
1.6
4.2
— — —
0.51
1.3
3.4
0.88
2.25
8.8
— — —
0.36
0.9
2.4
— — —
mAdc
Input Current I
in
15 ±0.1 ±0.00001 ±0.1 ±1.0 µAdc
Input Capacitance
(Vin = 0)
C
in
5.0 7.5 pF
Quiescent Current
(Per Package)
I
DD
5.0 10 15
— — —
5.0 10 20
— — —
0.005
0.010
0.015
5.0 10 20
— — —
150 300 600
µAdc
Total Supply Current**†
(Dynamic plus Quiescent, Per Package) (CL = 50 pF on all outputs, all buffers switching)
I
T
5.0 10 15
IT = (1.68 µA/kHz) f + I
DD
IT = (3.35 µA/kHz) f + I
DD
IT = (5.03 µA/kHz) f + I
DD
µAdc
#Data labelled “Typ” is not to be used for design purposes but is intended as an indication of the IC’s potential performance. **The formulas given are for the typical characteristics only at 25_C. †To calculate total supply current at loads other than 50 pF:
IT(CL) = IT(50 pF) + (CL – 50) Vfk
where: IT is in µA (per package), CL in pF, V = (VDD – VSS) in volts, f in kHz is input frequency, and k = 0.005.
PIN ASSIGNMENT
13
14
15
16
9
10
11
125
4
3
2
1
8
7
6
S2
S1
B1
A1
V
DD
C
out
S4
S3
B3
A3
B2
A2
V
SS
C
in
B4
A4
Page 3
MOTOROLA CMOS LOGIC DATA
3
MC14560B
SWITCHING CHARACTERISTICS* (C
L
= 50 pF, TA = 25_C)
Characteristic
Symbol V
DD
Min Typ # Max Unit
Output Rise and Fall Time
t
TLH
, t
THL
= (1.5 ns/pF) CL + 25 ns
t
TLH
, t
THL
= (0.75 ns/pF) CL + 12.5 ns
t
TLH
, t
THL
= (0.55 ns/pF) CL + 9.5 ns
t
TLH
, t
THL
5.0 10 15
— — —
100
50 40
200 100
80
ns
Propagation Delay Time
A or B to S
t
PLH
, t
PHL
= (1.7 ns/pF) CL + 665 ns
t
PLH
, t
PHL
= (0.66 ns/pF) CL + 297 ns
t
PLH
, t
PHL
= (0.5 ns/pF) CL + 195 ns
t
PLH
, t
PHL
5.0 10 15
— — —
750 330 220
2100
900 675
ns
A or B to C
out
t
PLH
, t
PHL
= (1.7 ns/pF) CL + 565 ns
t
PLH
, t
PHL
= (0.66 ns/pF) CL + 197 ns
t
PLH
, t
PHL
= (0.5 ns/pF) CL + 145 ns
5.0 10 15
— — —
650 230 170
1800
600 450
ns
Cin to C
out
t
PLH
, t
PHL
= (1.7 ns/pF) CL + 465 ns
t
PLH
, t
PHL
= (0.66 ns/pF) CL + 187 ns
t
PLH
, t
PHL
= (0.5 ns/pF) CL + 135 ns
5.0 10 15
— — —
550 220 160
1500
600 450
ns
Turn–Off Delay Time
Cin to S
t
PLH
= (1.7 ns/pF) CL + 715 ns
t
PLH
= (0.66 ns/pF) CL + 197 ns
t
PLH
= (0.5 ns/pF) CL + 215 ns
t
PLH
5.0 10 15
— — —
800 350 240
2250
975 750
ns
Turn–On Delay Time
Cin to S
t
PHL
= (1.7 ns/pF) CL + 565 ns
t
PHL
= (0.66 ns/pF) CL + 197 ns
t
PHL
= (0.5 ns/pF) CL + 145 ns
t
PHL
5.0 10 15
— — —
650 230 170
1800
600 450
ns
*The formulas given are for the typical characteristics only at 25_C. #Data labelled “Typ” is not to be used for design purposes but is intended as an indication of the IC’s potential performance.
Figure 1. Power Dissipation Waveforms
Duty Cycle = 50% All outputs connected to respective CL loads f = System clock frequency
Figure 2. Switching Time Waveforms
ALL INPUTS
ANY OUTPUT
20 ns
t
PLH
20 ns
V
DD
V
SS
V
OH
V
OL
90%
50%
10%
2f
1
t
PHL
V
DD
V
SS
V
OH
V
OL
20 ns20 ns
90%
50%
10%
90%
50%
10%
t
TLH
t
THL
ANY INPUT
ANY OUTPUT
Page 4
MOTOROLA CMOS LOGIC DATAMC14560B
4
FUNCTIONAL EQUIVALENT LOGIC DIAGRAM
C
in
A1
B1
A2
B2
A3
B3 A4
B4
7
15
14
1
2
3
4 5
6
VDD = PIN 16
VSS = PIN 8
13
C
out
12
11
10
9
S4
S3
S2
S1
Figure 3. Parallel Add/Subtract Circuit
One MC14560B and MC14561B permit a BCD digit to be added to or subtracted from a second digit, such as in this typical config­uration. A second MC14561B permits either digit to be added to or subtracted from the other, or either word to appear unmodified at the output.
X = Don’t Care
Zero Add/Subtract Result
0 0 B plus A 0 1 B minus A 1 X B
TRUTH TABLE
ADD/SUBTRACT
ZERO
B10
A10
B1
A1
MC14561B
MC14561B
MC14560B
MC14560B
F1
F2
F3
F4
A1
A3
A1A4 COMP COMP Z
F1
F2
F3
F4
A2 A3 A4 COMP COMP Z
A1
C
in
A2
A2
A3
A4
B1
B2
B3
B4
S3
S2
S1
S4
C
out
UNITS
A1
C
in
A2
A3
A4
B1
B2
B3
B4
S3
S2
S1
S4
C
out
TENS
Page 5
MOTOROLA CMOS LOGIC DATA
5
MC14560B
APPLICATIONS INFORMATION
INTRODUCTION
Frequently in small digital systems, simple decimal arith­metic is performed. Decimal data enters and leaves the sys­tem arithmetic unit in a binary coded decimal (BCD) format. The adder/subtracter in the arithmetic unit may be required to accept sign as well as magnitude, and generate sign, magnitude, and overflow. In the past, it has been cumber­some to build sign and magnitude adder/subtracters. Now, using Motorola’s MSI CMOS functions, the MC14560 NBCD Adders and MC14561 9’s Complementers, NBCD adder/ subtracters may be built economically, with surprisingly low package count and moderate speed.
Some background information on BCD arithmetic is pres­ented here, followed by simple circuits for unsigned adder/ subtracters. The final circuit discussed is an adder/subtracter for signed numbers with complete overflow and sign correc­tion logic.
DECIMAL NUMBER REPRESENTATION
Because logic elements are binary or two–state devices, decimal digits are generally represented as a group of bits in a weighted format. There are many possible binary codes which can be used to represent a decimal number. One of the most popular codes using 4 binary digits to represent 0 thru 9 is Natural Binary Coded Decimal (NBCD or 8–4–2–1 code).
NBCD is a weighted code. If a value of “0” or “1” is as­signed to each of the bit positions, where the rightmost posi­tion is 20 and the leftmost is 23, and the values are summed for a given code, the result is equal to the decimal digit repre­sented by the code. Thus, 01 10 equals 0@23 + 1@22 + 1@21 + 0@20 = 4 + 2 = 6. The 1010, 1011, 1100, 1101, 1110, and 1111 binary codes are not used. Because of these illegal states, the addition and subtraction of NBCD numbers is more com­plex than similar calculations on straight binary numbers.
ADDITION OF UNSIGNED NBCD NUMBERS
When 2 NBCD digits, A and B, and a possible carry , C, are added, a total of 20 digit sums (A + B + C) are possible as shown in Table 1.
The binary representations for the digit sums 10 thru 19 are offset by 6, the number of unused binary states, and are not correct. An algorithm for obtaining the correct sum is shown in Figure 1. A conventional method of implementing the BCD addition algorithm is shown in Figure 2(a). The NBCD digits, A and B, are summed by a 4 bit binary full ad­der. The resultant (sum and carry) is input to a binary/BCD code converter which generates the correct BCD code and carry.
An NBCD adder block which performs the above function is a vailable in a s ingle C MOS p ackage ( MC14560).
Figure 2(b) shows n decades cascaded for addition of n digit unsigned NBCD numbers. Add time is typically 0.1 + 0.2n µs for n decades. When the carry out of the most significant de­cade is a logical “1”, an overflow is indicated.
COMPLEMENT ARITHMETIC
Complement arithmetic is used in NBCD subtraction. That is, the “complement” of the subtrahend is added to the minu­end. The complementing process amounts to biasing the subtrahend such that all possible sums are positive. Consid­er the subtraction of the NBCD numbers, A and B:
R = A – B
where R is the result. Now bias both sides of the equation by 10N – 1 where N is the number of digits in A and B.
R + 10N – 1 A – B + 10N – 1
Rearranging,
R + 10N – 1 A + (10N – 1 – B)
The term (10N – 1 – B), – B biased by 10N – 1, is known as the 9’s complement of B. When A > B, R + 10N – 1 > 10N – 1; thus R is a positive number. To obtain R, 1 is added to R + 10N – 1, and the carry term, 10N, is dropped. The addition of 1 is called End Around Carry (EAC).
When A < B, R + 10N – 1 < 10N – 1, no EAC results and R is a negative number biased by 10N – 1; thus R + 10N – 1 is the 9’s complement of R.
SUBTRACTION OF UNSIGNED NBCD NUMBERS
Nine’s complement arithmetic requires an element to per­form the complementing function. An NBCD 9’s comple­menter may be implemented using a 4 bit binary adder and 4 inverters, or with combinatorial logic. The Motorola MC14561 9’s complementer is available in a single package. It has true and inverted complement disable, which allow straight– through or complement modes of operation. A “zero” line forces the output to “0”. Figure 3 shows an NBCD subtracter block using the MC14560 and MC14561. Also shown are n cascaded blocks for subtraction of n digit unsigned numbers. Subtract time is 0.6 + 0.4n µs for n stages. Underflow (bor­row) is indicated by a logical “0” on the carry output of the most significant digit. A “0” carry also indicates that the differ­ence is a negative number in 9’s complement form. If the re­sult is input to a 9’s complementer, as shown, and its mode controlled by the carry out of the most significant digit, the output of the complementer will be the correct negative mag­nitude. Note that the carry out of the most significant digit (MSD) is the input to c arry in of the least significant digit (LSD). This End Around Carry is required because subtrac­tion is done in 9’s complement arithmetic.
By controlling the complement and overflow logic with an add/subtract line, both a ddition and subtraction are p er­formed using the basic subtracter blocks (Figure 4).
Page 6
MOTOROLA CMOS LOGIC DATAMC14560B
6
Table 1. Sum = A + B + C
Binary Sums
Decimal
Numbers
Corrected
Binary Sums
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 Non valid 1101 BCD 1110 representation 1111 0000 + Carry 0001 + Carry 0010 + Carry 0011 + Carry
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19
0000 0001 0010 0011 0100 0101 0110 0111 1000
1001 0000 + Carry 0001 + Carry 0010 + Carry 0011 + Carry 0100 + Carry 0101 + Carry 0110 + Carry 0111 + Carry 1000 + Carry 1001 + Carry
ADDITION AND SUBTRACTION OF SIGNED NBCD NUMBERS
Using MC14560 NBCD Adders and MC14561 9’s Comple­menters, a sign and magnitude adder/subtracter can be con­figured (Figure 5). Inputs A and B are signed positive (AS, B
S
= “0”) or negative (AS, BS = “1”). B is added to or subtracted from A under control of an Add/Sub line (subtraction = “1”). The result, R, of the operation is positive signed, positive signed with overflow, negative signed, or negative signed with overflow. Add/subtract time is typically 0.6 + 0.4n µs for n decades.
An exclusive–OR of Add/Sub line and BS produces B′, which controls the B complementers. If BS, the sign of B, is a logical “1” (B is negative) and the Add/Sub line is a “0” (add B to A), then the output of the exclusive–OR (BS′) is a logical “1” and B is complemented. If BS = “1” and Add/Sub = “1”, B is not complemented since subtracting a negative number is the same as adding a positive number. When Add/Sub is a “1” and BS = “0”, BS′ is a “1” and B is complemented. The A complementer is controlled by the A sign bit, AS. When AS = “1”, A is complemented.
Figure 4. Unsigned NBCD Addition Algorithm
6,941 5,870
+
4 BIT BINARY FULL ADDER
DIGIT BINARY SUMS
BINARY SUMS WITH CARRY FROM CONVERTERS
CODE CONVERTERS
CORRECTED SUM
12,811
A B
C
in
C
out
BINARY TO NBCD
CODE CONVERTER
RESULT, R
A1 B1 A2 B2 A
n
B
n
C
in
C
in
C
in
C
out
C
out
C
out
R1 R2 R
n
OVERFLOW
THOUSANDS
0110 0101
HUNDREDS
1001 1000
TENS
0100 0111
UNITS
0001 0000
ADDER
C
in
ADDER
C
in
ADDER
C
in
ADDER
1 1 0
1011 0001 1011 00011 1100 0010 1011 0001
1
C
out
C
out
C
out
C
out
1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1
Figure 5. Addition of Unsigned NBCD Numbers
(a) MC14560 Block Diagram (b) n–Decade Adder
Typical Add T ime = 0.1 + 0.2n µs where n = Number of Decades
4 BIT BINARY ADDERS
MC14560 MC14560 MC14560
Page 7
MOTOROLA CMOS LOGIC DATA
7
MC14560B
The truth table and Karnaugh maps for sign, overflow, and End Around Carry are shown in Figures 6 and 7. Note the use of BS′ from the exclusive–OR of Add/Sub and BS. BS′ eliminates Add/Sub as a variable in the truth table. As an ex­ample of truth table generation, consider an n decade adder/ subtracter where AS = “0”, BS = “1”, and Add/Sub = “0”. B is in 9’s complement form, 10N – 1 – B. Thus A + (10N – 1 – B) = 10N – 1 + (A – B). There is no carry when A v B, and the sign is negative (sign = “1”). When AS and BS are opposite states and Add/Sub is a “0” (add mode), no overflow can oc­cur (overflow = “0”). The other output states are determined in a similar manner (see Figure 6).
From the Karnaugh maps it is apparent that End Around Carry is composed of the two symmetrical functions S2 and S3 of three variables with AS BS′ C
out
as the center of sym­metry. This i s the definition of t he majority l ogic function M3(ABC). Similarly the Sign is composed of the symmetrical functions S2(3) and S3(3) but with the center of symmetry
translated to ASBS′ C
out
. This is equivalent to the majority
function M3(ASBS′ C
out
). Further evaluation of the maps and truth table reveal that Overflow can be generated by the exclusive–OR function of End Around Carry and Carry Out. This analysis results in a minimum device count consisting of one exclusive–OR package and one dual Majority Logic package to implement BS′, EAC, Sign and Overflow. The logic connections of these devices are shown in Figure 5.
The output sign, RS, complements the result of the add/ subtract operation when RS = “1”. This is required because the adder performs 9’s complement arithmetic. Complement­ing, when RS indicates the result is negative, restores sign and magnitude convention.
Several variations of the adder/subtracter are possible. For example, 9’s complement is available at the output of the NBCD adders, and output complementers are eliminated if sign and magnitude output is not required.
Figure 6. Subtraction of Unsigned NBCD Numbers
A B
V
DD
Z
C
C
A1 A2 A3 A4
F1 F2 F3 F4
C
n
C
in
A1 A2 A3 A4 B1 B2 B3 AB
C
out
C
n + 1
S1 S2 S3 S4
MC14560
A1 A2 A3 A4
Z
C
C
V
DD
F1 F2 F3 F4
MC14561
FROM C
out
OF MOST SIGNIFICANT
DECADE
RESULT, R
LEAST
SIGNIFICANT
DECADE
A1 B1 A2 B2 A
n
B
n
MOST
SIGNIFICANT
DECADE
C
in
C
C
out
C
in
C
C
out
C
in
C
C
out
R1 R2 R
n
“0” INDICATES UNDERFLOW
(NEGATIVE RESULT)
(a) Basic Subtracter Block
(b) n–Decade Subtracter
Typical Subtract Time = 0.6 + 0.4n µs where n = Number of Decades
MC14561
BASIC
SUBTRACT
BLOCK
R1
Page 8
MOTOROLA CMOS LOGIC DATAMC14560B
8
SUMMARY
The concepts of binary code representations for decimal numbers, addition, and complement subtraction were dis­cussed in detail. Using the basic Adder and Complementer MSI blocks, adder/subtracters for both signed and unsigned numbers were illustrated with examples.
REFERENCES
1. Chu, Y.:
Digital Computer Design Fundamentals
, New
York, McGraw–Hill, 1962.
2.
McMOS Handbook
, Motorola Inc., 1st Edition.
3. Beuscher, H.:
Electronic Switching Theory and Circuits
,
New York, Van Nostrand Reinhold, 1971.
4. Garrett, L.: CMOS May Help Majority Logic Win De­signer’s Vote,
Electronics
, July 19, 1973.
5. Richards, R.:
Digital Design
, New York, Wiley–
Interscience, 1971.
Figure 7. Adder/Subtracter for Unsigned NBCD Numbers
A1 B1 A2 B2 A
n
B
n
C
in
C
C
out
C
in
C
C
out
C
in
C
C
out
R1 R2 R
n
MSD
BASIC
SUBTRACT
BLOCK
LSD
ADD/SUBTRACT
(“1”/“0”)
1/6 MC14572
1/6 MC14572
OVERFLOW = “1”
UNDERFLOW = “1”
(NEGATIVE RESULT)
Typical Add/Subtract Time = 0.6 + 0.4 n µs
where n = Number of Decades
Page 9
MOTOROLA CMOS LOGIC DATA
9
MC14560B
Figure 8. Sign and Magnitude Adder/Subtracter with Overflow
B
n
A
n
B2A2
MC14561MC14561MC14561MC14561
MC14560MC14560
MC14561MC14561
R
n
R2
C
out
C
out
OVERFLOW
SIGN OF R
S
1/4 MC14070
SIGN
Z
Z
W
W
V
DD
EAC
B1A1
MC14561MC14561
M
5
M
5
MC14561
MC14560
C
out
MC14530
A
B
C
D
E
A
B
C
D
E
CCZ
R1
A1 A2 A3 A4
F1 F2 F3 F4
A1 A2 A3 A4 B1 B2 B3 B4
S1 S2 S3 S4
A1 A2 A3 A4
F1 F2 F3 F4
A1 A2 A3 A4
F1 F2 F3 F4
CCZ
C
in
1/4 MC14070
1/4 MC14070
B
S
V
DD
A
S
B
S
ADD/SUB
Typical Add/Subtract Time = 0.6 + 0.4n s
where n = Number of Decades
µ
CCZ
Page 10
MOTOROLA CMOS LOGIC DATAMC14560B
10
Inputs
Arithmatic Expression
for R* (Result)
Outputs
(N = Number of Digits,
10N = Modulus
End Around
A
S
“1” = Neg
BS′
“1” = Neg
C
out
“1” = Carry
A, B, R are Positive
Magnitudes)
Carry (EAC)
“1” = EAC
Sign of R
“1” = Negative
Overflow
“1” = Overflow
0 0 0
R = A + 8
No EAC (“0”) because R is correct result.
Since A and B are positive signed, R is positive signed (“0”).
When C
out
= “0”, there is no carry (R < 10N) and thus no overflow (“0”).
0 0 1
When C
out
= “1”, there is a carry (R 10N) and thus overflow (“1”).
0 1 0
R = A – B
= A + (10N – 1 – B) = A – B + 10N – 1
No EAC (“0”) because 9’s complement expression for R is correct result.
A v B when C
out
= “0”; thus sign of R must be negative (“1”).
0 1 1
EAC = “1” because expression for R is in error by 1.
A > B when C
out
= “1”; thus sign of R must be positive (“0”).
There is never an overflow when
1 0 0
R = B – A
= B + (10N – 1 – A) = B – A + 10N – 1
No EAC (“0”) because 9’s complement expression for R is correct result.
B v A when C
out
= “0”; thus sign of R must be negative (“1”).
overflow when numbers of opposite sign are added.
1 0 1
EAC = “1” because expression for R is in error by 1.
B > A when C
out
= “1”; thus sign of R must be positive (“0”).
1 1 0
R = – A – B
= (10N – 1 – A) +
(10N – 1 – B)
= – (A + B) + 2 x
EAC = “1” because 9’s complement expression for R is in error by 1.
Since A and B are negative signed. R is negative signed (“1”).
When C
out
= “0”, there is no Carry (R < 0N) and (A + B) > 10N – 1 indicating overflow (“1”).
1 1 1
10N – 2
When C
out
= “1”, there is a carry (R 10N) and (A + B) v 10N – 1 indicating no overflow (“0”).
*Output of Adders
Figure 9. Truth Table Generation for EAC, Sign, and Overflow Logic
Page 11
MOTOROLA CMOS LOGIC DATA
11
MC14560B
TRUTH TABLE
Inputs Outputs
A
S
BS′ C
out
EAC SGN OVF
0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0
BS = (Add/Sub) ę B
S
AS = Sign of A (“1” = Negative) BS = Sign of B (“1” = Negative) C
out
= Adder Carry Out
Figure 10. Mapping of EAC, Sign and Overflow Logic
0 1 1 1 0 1
0* 0
End Around Carry
A
S
C
out
B
S
1 1 0 1
0* 0
0 1
Sign (SGN)
A
S
C
out
B
S
0 1 0 0 1 0 0 0
Overflow (OVF)
A
S
C
out
B
S
*= Center of Symmetry
EAC = S2 (ASBS′ C
out
) + S3 (ASBS′ C
out
)
= M3 (ASBS′ C
out
)
SGN = S2 (ASBS′ C
out
) + S3 (ASBS′ C
out
)
= M3 (ASBS′ C
out
)
0 1 1 1 0 1 0 0
EAC
0 0 1 1 1 1 0 0
C
out
0 1 0 0 1 0 0 0
OVF
ę
=
ę
=
KARNAUGH MAPS
Page 12
MOTOROLA CMOS LOGIC DATAMC14560B
12
OUTLINE DIMENSIONS
P SUFFIX
PLASTIC DIP PACKAGE
CASE 648–08
ISSUE R
NOTES:
1. DIMENSIONING AND TOLERANCING PER ANSI Y14.5M, 1982.
2. CONTROLLING DIMENSION: INCH.
3. DIMENSION L TO CENTER OF LEADS WHEN FORMED PARALLEL.
4. DIMENSION B DOES NOT INCLUDE MOLD FLASH.
5. ROUNDED CORNERS OPTIONAL.
–A–
B
F
C
S
H
G
D
J
L
M
16 PL
SEATING
1 8
916
K
PLANE
–T–
M
A
M
0.25 (0.010) T
DIM MIN MAX MIN MAX
MILLIMETERSINCHES
A 0.740 0.770 18.80 19.55 B 0.250 0.270 6.35 6.85 C 0.145 0.175 3.69 4.44 D 0.015 0.021 0.39 0.53 F 0.040 0.70 1.02 1.77 G 0.100 BSC 2.54 BSC H 0.050 BSC 1.27 BSC J 0.008 0.015 0.21 0.38 K 0.110 0.130 2.80 3.30 L 0.295 0.305 7.50 7.74 M 0 10 0 10 S 0.020 0.040 0.51 1.01
____
L SUFFIX
CERAMIC DIP PACKAGE
CASE 620–10
ISSUE V
NOTES:
1. DIMENSIONING AND TOLERANCING PER ANSI Y14.5M, 1982.
2. CONTROLLING DIMENSION: INCH.
3. DIMENSION L TO CENTER OF LEAD WHEN FORMED PARALLEL.
4. DIMENSION F MAY NARROW TO 0.76 (0.030) WHERE THE LEAD ENTERS THE CERAMIC BODY.
–A–
–B–
–T–
F
E
G
N
K
C
SEATING PLANE
16 PLD
S
A
M
0.25 (0.010) T
16 PLJ
S
B
M
0.25 (0.010) T
M
L
DIM MIN MAX MIN MAX
MILLIMETERSINCHES
A 0.750 0.785 19.05 19.93 B 0.240 0.295 6.10 7.49 C ––– 0.200 ––– 5.08 D 0.015 0.020 0.39 0.50 E 0.050 BSC 1.27 BSC F 0.055 0.065 1.40 1.65 G 0.100 BSC 2.54 BSC H 0.008 0.015 0.21 0.38 K 0.125 0.170 3.18 4.31 L 0.300 BSC 7.62 BSC M 0 15 0 15 N 0.020 0.040 0.51 1.01
_ _ _ _
16 9
1 8
Page 13
MOTOROLA CMOS LOGIC DATA
13
MC14560B
OUTLINE DIMENSIONS
D SUFFIX
PLASTIC SOIC PACKAGE
CASE 751B–05
ISSUE J
NOTES:
1. DIMENSIONING AND TOLERANCING PER ANSI Y14.5M, 1982.
2. CONTROLLING DIMENSION: MILLIMETER.
3. DIMENSIONS A AND B DO NOT INCLUDE MOLD PROTRUSION.
4. MAXIMUM MOLD PROTRUSION 0.15 (0.006) PER SIDE.
5. DIMENSION D DOES NOT INCLUDE DAMBAR PROTRUSION. ALLOWABLE DAMBAR PROTRUSION SHALL BE 0.127 (0.005) TOTAL IN EXCESS OF THE D DIMENSION AT MAXIMUM MATERIAL CONDITION.
1 8
16 9
SEATING
PLANE
F
J
M
R
X 45
_
G
8 PLP
–B–
–A–
M
0.25 (0.010) B
S
–T–
D
K
C
16 PL
S
B
M
0.25 (0.010) A
S
T
DIM MIN MAX MIN MAX
INCHESMILLIMETERS
A 9.80 10.00 0.386 0.393 B 3.80 4.00 0.150 0.157 C 1.35 1.75 0.054 0.068 D 0.35 0.49 0.014 0.019 F 0.40 1.25 0.016 0.049 G 1.27 BSC 0.050 BSC J 0.19 0.25 0.008 0.009 K 0.10 0.25 0.004 0.009 M 0 7 0 7 P 5.80 6.20 0.229 0.244 R 0.25 0.50 0.010 0.019
_ _ _ _
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MC14560B/D
*MC14560B/D*
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