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

Module 13 − Introduction to Number Systems and Logic

Pages i, 1−1, 1−11, 1−21, 1−31, 1−41, 1−51, 1−61, 2−12−11, 2−21, 2−31, 3−1, 3−11, 3−21, 3−31, 3−41, Index

 

 

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

NEETS Modules
- Matter, Energy, and Direct Current
- Alternating Current and Transformers
- Circuit Protection, Control, and Measurement
- Electrical Conductors, Wiring Techniques, and Schematic Reading
- Generators and Motors
- Electronic Emission, Tubes, and Power Supplies
- Solid-State Devices and Power Supplies
- Amplifiers
- Wave-Generation and Wave-Shaping Circuits
- Wave Propagation, Transmission Lines, and Antennas
- Microwave Principles
- Modulation Principles
- Introduction to Number Systems and Logic Circuits
- - Introduction to Microelectronics
- Principles of Synchros, Servos, and Gyros
- Introduction to Test Equipment
- Radio-Frequency Communications Principles
- Radar Principles
- The Technician's Handbook, Master Glossary
- Test Methods and Practices
- Introduction to Digital Computers
- Magnetic Recording
- Introduction to Fiber Optics
Note: Navy Electricity and Electronics Training Series (NEETS) content is U.S. Navy property in the public domain.