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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: 
 
Q107.
 
     BCD Conversion Problem - RF Cafe

 Q108.
 
     BCD Conversion Problem - RF Cafe
 
 Q109.
 
     BCD Conversion Problem - RF Cafe
 

 

1-61


 
 
Q110.

     BCD Conversion Problem - RF Cafe

SUMMARY

 

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.

 

POSITIONAL NOTATION - RF Cafe

 

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

 

MOST SIGNIFICANT DIGIT (MSD) - RF Cafe

 

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

 

 

1-62


 

 

LEAST SIGNIFICANT DIGIT (LSD) - RF Cafe

 

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.

 

BINARY NUMBER SYSTEM - RF Cafe

 

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.

 

 

1-63


 

 

CONVERT A WHOLE BASE 10 NUMBER - RF Cafe

 

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).

 

CONVERT DECIMAL FRACTIONS - RF Cafe

 

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

 

 

1-64


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

 

ANSWERS TO QUESTIONS Q1. THROUGH Q110.

 

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
 
A8.
 
    (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

 

 

1-65


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

 

 

1-66


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

 

 

1-67


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

 

 

1-68


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

 

 

1-69



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