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Digital Electronics
Principles & Applications
Seventh Edition.
Roger L. Tokheim.
Numbers We Use in
Digital Electronics.
(C)2008 The McGraw-Hill Companies, Inc. All rights reserved.
Counting in Decimal and Binary
Place Value
Binary to Decimal Conversion
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Digital Electronics Principles & Applications Seventh Edition
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Digital Electronics Principles & Applications Seventh Edition Roger L. Tokheim Chapter
2 Numbers We Use in Digital Electronics (C)2008 The McGraw-Hill Companies, Inc. All rights reserved. Counting in Decimal and Binary Place Value Binary to Decimal Conversion Decimal to Binary Conversion Electronic Translators Hexadecimal Numbers Octal Numbers Bits, Bytes and Words INTRODUCTION Counting in Decimal and Binary Number System -
Code using symbols that refer to
a number of items. Decimal Number System - Uses ten symbols (base 10 system) Binary System -
Uses two symbols (base 2 system) QUIZ binary 1.
The __________ (binary, octal) number system uses only the symbols 0 and 1 in counting. decimal 2.
The __________ (decimal, hexadecimal) number system uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. binary 3.
The __________ (binary, decimal) number system is also called the base 2 system because it uses only two symbols to represent numbers.
Place Value Numeric value of symbols in different positions. Example - Place value in binary system: 2s Place Value 8s 4s 1s Binary Yes Yes No No Number 1 1 0 0 RESULT:
Binary 1100 = decimal 8 + 4 + 0 + 0 = decimal 12
Binary to Decimal Conversion Convert Binary Number 110011 to a Decimal Number: Binary 1
51 Decimal QUIZ Convert the following binary numbers into decimal numbers: 9 Binary
= 15 Binary
= 2 Binary
= Decimal to Binary Conversion Divide by 2 Process Decimal # 13 ÷
remainder 1 6
remainder 0 3
remainder 1
Divide-by-2 Process Stops When Quotient Reaches 0 1
0 remainder 1 1 1 0 1 QUIZ Convert the following decimal numbers into binary: 1011 Decimal
= 0100 Decimal
= 10001 Decimal
= Electronic Translators Devices that convert from decimal to binary numbers and from binary to decimal numbers. Encoders -
translates from decimal to binary Decoders -
translates from binary to decimal 3 Electronic Encoder –
to Binary Binary output Decimal input 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 Decimal to Binary Encoder 7 5 0 Encoders are available in IC form. This encoder translates from decimal
input to binary (BCD) output. Electronic Decoding –
Binary to Decimal Binary input Decimal output 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 Binary-to- 7-Segment Decoder/ Driver Electronic decoders are available in IC form.
This decoder translates from binary to decimal.
Decimals are shown on an 7-segment LED display.
This decoder also drives the 7-segment display. QUIZ 1.
The general name for an electronic device that translates from binary to decimal is a(n) __________. decoder 2.
The general name for an electronic device that translates from decimal to binary is a(n) __________. encoder encoder 3.
An electronic device called a(n) __________ (decoder, encoder) would probably be located between the keypad of a calculator and its processing circuitry to translate from decimal to machine language (binary). Hexadecimal Number System Uses16symbols - Base16System 0-9, A, B, C, D, E, F
Binary 0001 1001 1010 1111 10000 Hexadecimal 1 9 A F 10 Decimal 1 9 10 15 16 Hexadecimal and Binary Conversions Hexadecimal to Binary Conversion
HexadecimalC
Binary1100
0011 Binary to Hexadecimal Conversion Binary 1110
1010 Hexadecimal
A Decimal to Hexadecimal Conversion Divide by16Process Decimal # 47÷16 = 2
remainder 15 Divide-by-2 Process Stops When Quotient Reaches 0 2÷16 =0
remainder 2 2 F Hexadecimal to Decimal Conversion Convert hexadecimal number 2DB to a decimal number 256s16s1s Place Value 2
B Hexadecimal (256 x 2)(16 x 13)(1 x 11) 512
=731 Decimal QUIZ Convert Hexadecimal numberA6to Binary A6 = 1010
0110 (Binary) Convert Hexadecimal number16to Decimal 16 = 22 (Decimal) Convert Decimal63to Hexadecimal 63 = 3F (Hexadecimal) Octal Numbers Uses 8 symbols - Base 8 System 0, 1, 2, 3, 4, 5, 6, 7
Decimal 1 6 7 8 9 Binary 001 110 111 001 000 001 001 Octal 1 6 7 10 11 QUIZ 111 The octal number 7 equals ______ in binary. 2.
The octal number 11 equals ______ in binary. 001 001 010 111 3.
The decimal number 23 equals ______ in binary. 27 4.
The decimal number 23 equals ______ in octal. 011 111 5.
The octal number 37 equals ______ in binary. 31 6.
The octal number 37 equals ______ in decimal. Practical Suggestion on
Number System
Conversions
Use a scientific calculator
Most scientific calculators have DEC, BIN,
OCT, and HEX modes and can either
convert between codes or perform
arithmetic in different number systems.
Most scientific calculators also have other
functions that are valuable in digital
electronics such as AND, OR, NOT,
XOR, and XNOR logic functions.
Groupings of Binary Digits Bit1-bit (0 or 1) Nibble4-bits (such as 1101) Byte8-bits (such as ) Word16-bits (common definition) Double-word32-bits Quad-word64-bits QUIZ A 4-bit grouping of binary digits is called a _____ (byte, nibble). nibble 2.
An byte refers to an a(n) _____ (8, 64)-bit group of binary digits. 8 3.
A single binary digit (such as a 0 or 1) is called a _____ (bit, nibble). bit 4.
A common definition for a word in computer jargon is a _____ (1, 16)-bit group of binary digits. 16 Counting in Decimal and Binary Place Value Binary to Decimal Conversion Decimal to Binary Conversion Electronic Translators Hexadecimal Numbers Octal Numbers Bits, Bytes and Words REVIEW
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