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Module 13 - Introduction to Number Systems and Logic
Navy Electricity and Electronics Training Series (NEETS)
Chapter 1:  Pages 1-61 through 1-69



BCD Conversion - RF Cafe


In this case, the higher order group is invalid, but the lower order group is valid. Therefore, the correction factor is added only to the higher order group as shown:


BCD Conversion - RF Cafe


Convert this total to decimal to check your answer:


BCD Conversion - RF Cafe


Remember that the correction factor is added only to groups that exceed 910  (1001BCD). Convert the following numbers to BCD and add: 
     BCD Conversion Problem - RF Cafe

     BCD Conversion Problem - RF Cafe
     BCD Conversion Problem - RF Cafe




     BCD Conversion Problem - RF Cafe



Now that you've completed this chapter, you should have a basic understanding of number systems. The number systems that were dealt with are used extensively in the microprocessor and computer fields. The following is a summary of the emphasized terms and points found in the "Number Systems" chapter.

The UNIT represents a single object.
A NUMBER is a symbol used to represent one or more units.
The RADIX is the base of a positional number system. It is equal to the number of symbols used in that number system.
A POSITIONAL NOTATION is a system in which the value or magnitude of a number is defined not only by its digits or symbol value, but also by its position. Each position represents a power of the radix, or base, and is ranked in ascending or descending order.




The MOST SIGNIFICANT DIGIT (MSD) is a digit within a number (whole or fractional) that has the largest effect (weighing power) on that number.




The LEAST SIGNIFICANT DIGIT (LSD) is a digit within a number (whole or fractional) that has the least effect (weighting power) on that number.








The BINARY NUMBER SYSTEM is a base 2 system. The symbols 1 and 0 can be used to represent the state of electrical/electronic devices. A binary 1 may indicate the device is active; a 0 may indicate the device is inactive.




The OCTAL NUMBER SYSTEM is a base 8 system and is quite useful as a tool in the conversion of binary numbers. This system works because 8 is an integral power of 2; that is, 23  = 8. The use of octal numbers reduces the number of digits required to represent the binary equivalent of a decimal number.

The HEX NUMBER SYSTEM is a base 16 system and is sometimes used in computer systems. A binary number can be converted directly to a base 16 number if the binary number is first broken into groups of four digits.
The basic rules of ADDITION apply to each of the number systems. Each system becomes unique when carries are produced.
SUBTRACTION in each system is based on certain rules of that number system. The borrow varies in magnitude according to the number system in use. In most computers, subtraction is accomplished by using the complement (R's or R's-1) of the subtrahend and adding it to the minuend.
To CONVERT A WHOLE BASE 10 NUMBER to another system, divide the decimal number by the base of the number system to which you are converting. Continue dividing the quotient of the previous division until it can no longer be done. Extract the remainders - the remainder from the first computation will yield the LSD; the last will provide the MSD.








To CONVERT DECIMAL FRACTIONS, multiply the fraction by the base of the desired number system. Extract those digits that move to the left of the radix point. Continue to multiply the fractional product for as many places as needed. The first digit left of the radix point will be the MSD, and the last will be the LSD. The example to the right shows the process of converting 248.3210  to the octal equivalent (370.2438).




BINARY numbers are converted to OCTAL and HEX by the grouping method. Three binary digits equal one octal digit; four binary digits equal one hex digit.


BINARY numbers to OCTAL and HEX - RF Cafe




To CONVERT binary, octal, and hex numbers to DECIMAL use the POWERS of the base being converted.


CONVERT binary, octal, and hex numbers to DECIMAL - RF Cafe


BINARY-CODED DECIMAL (BCD) is a coding system used with some microprocessors. A correction factor is needed to correct invalid numbers




A1.     Unit
A2.     Number
A3.     Arabic
A4.     The number of symbols used in the system
A5.     17310
A6.     103, 102, 101, 100
A7.           Radix point
    (a)  MSD - 4, LSD - 0
    (b)  MSD - 1, LSD - 6
    (c)  MSD - 2, LSD - 4
    (d)  MSD - 2, LSD - 1
A9.     111112
A10.    111012
A11.    1000012
A12.    1011112
A13.    10002




A14.    110111102
A15.    100002
A16.    10112
A17.    111012
A18.    112
A19.    11102
A20.    111112
A21.    22110
A22.    011000112
A23.    -00012
A24.    108
A25.    608
A26.    10158
A27.    223068
A28.    1518
A29.    248
A30.    3218
A31.    368
A32.    3368
A33.    3778
A34.    1048
A35.    77678
A36.    DD8D16
A37.    11FDB16
A38.    125F16
A39.    1202016
A40.    191AB16
A41.    1AA816
A42.    33516




A43.    93516
A44.    953116
A45.    36B316
A46.    10ABC16
A47.    42F0F16
A48.    10010002
A49.    11000012
A50.    111100112
A51.    0.11102
A52.    0.01012
A53.    10001.011012
A54.     78
A55.    538
A56.    7638
A57.    0.74678
A58.    0.002038
A59.    374.1278
A60.    2A16
A61.    5316
A62.    B016
A63.    1EB16
A64.    0.B89316
A65.    28
A66.    128
A67.    578
A68.    0.148
A69.    0.638
A70.    67.258
A71.    216




A72.    B16
A73.    2F16
A74.    0.316
A75.    0.CC16
A76.    37.5416
A77.    1110112
A78.    1010010102
A79.    1000000112
A80.    0.1001011102
A81.    0.1110112
A82.    11110.1012
A83.    3C16
A84.    14A16
A85.    0.0C16
A86.    C.8816
A87.    1000112; 438
A88.    110112; 338
A89.    0.1110012; 0.718
A90.    1000101.1012; 105.58
A91.    1810
A92.    12410
A93.    8510
A94.    0.312510
A95.    0.62510
A96.    109.937510
A97.    1510
A98.    5210
A99.    25310
A100.    0.510




A101.    0.76562510
A102.    8.2812510
A103.    3610
A104.    16510
A105.    21910
A106.    998.312510
A107.    1000BCD
A108.    1001BCD
A109.    0001 0001BCD
A110.    0010 0010BCD




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