2INTRODUCTION Counting in Decimal and Binary Place Value Binary to Decimal ConversionDecimal to Binary ConversionElectronic TranslatorsHexadecimal NumbersOctal NumbersBits, Bytes and Words
3Counting in Decimal and Binary Number System -Code using symbols that refer toa number of items.Decimal Number System -Uses ten symbols (base 10 system)Binary System -Uses two symbols (base 2 system)
4QUIZ1. The __________ (binary, octal) number system uses only the symbols 0 and 1 in counting.binarydecimal2. The __________ (decimal, hexadecimal) number system uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.3. The __________ (binary, decimal) number system is also called the base 2 system because it uses only two symbols to represent numbers.binary
5Place Value Numeric value of symbols in different positions. Example - Place value in binary system:Place Value8s4s2s1sBinaryYesYesNoNoNumber11RESULT: Binary 1100 = decimal = decimal 12
6Binary to Decimal Conversion Convert Binary Number to a Decimal Number:BinaryDecimal= 51
7QUIZ 9 Binary 1001 = 15 Binary 1111 = 2 Binary 0010 = Convert the following binary numbers into decimal numbers:9Binary =15Binary =2Binary =
9QUIZConvert the following decimal numbers into binary:Decimal =10110100Decimal =10001Decimal =
10Electronic Translators Devices that convert from decimal to binary numbers and from binary to decimal numbers.Encoders -translates from decimal to binaryDecoders -translates from binary to decimal
11Electronic Encoder – Decimal to Binary Binary outputDecimal inputDecimaltoBinaryEncoder375Encoders are available in IC form.This encoder translates from decimal input to binary (BCD) output.
12Electronic Decoding – Binary to Decimal Binary inputDecimal outputBinary-to-7-SegmentDecoder/DriverElectronic 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.
13QUIZ1. The general name for an electronic device that translates from binary to decimal is a(n) __________.decoder2. The general name for an electronic device that translates from decimal to binary is a(n) __________.encoder3. 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).encoder
14Hexadecimal Number System Uses 16 symbols - Base 16 System0-9, A, B, C, D, E, FDecimal19101516Binary000110011010111110000Hexadecimal19AF10
15Hexadecimal and Binary Conversions Hexadecimal to Binary ConversionHexadecimal C 3BinaryBinary to Hexadecimal ConversionBinaryHexadecimal E A
17Hexadecimal to Decimal Conversion Convert hexadecimal number 2DB to a decimal number256s 16s 1sPlace ValueD BHexadecimal(256 x 2) (16 x 13) (1 x 11)= 731Decimal
18QUIZ Convert Hexadecimal number A6 to Binary A6 = Convert Hexadecimal number 16 to Decimal16 =22 (Decimal)Convert Decimal 63 to Hexadecimal63 =3F (Hexadecimal)
19Uses 8 symbols - Base 8 System Octal NumbersUses 8 symbols - Base 8 System0, 1, 2, 3, 4, 5, 6, 7Decimal16789Binary001110111Octal1671011
20QUIZThe octal number 7 equals ______ in binary.1112. The octal number 11 equals ______ in binary.3. The decimal number 23 equals ______ in binary.4. The decimal number 23 equals ______ in octal.275. The octal number 37 equals ______ in binary.6. The octal number 37 equals ______ in decimal.31
21Practical Suggestion on Number System Conversions Use a scientific calculatorMost scientific calculators have DEC, BIN,OCT, and HEX modes and can eitherconvert between codes or performarithmetic in different number systems.Most scientific calculators also have otherfunctions that are valuable in digitalelectronics such as AND, OR, NOT,XOR, and XNOR logic functions.
22Groupings of Binary Digits Bit 1-bit (0 or 1)Nibble 4-bits (such as 1101)Byte 8-bits (such as )Word 16-bits (common definition)Double-word 32-bitsQuad-word 64-bits
23QUIZA 4-bit grouping of binary digits is called a _____ (byte, nibble).nibble2. An byte refers to an a(n) _____ (8, 64)-bit group of binary digits.83. A single binary digit (such as a 0 or 1) is called a _____ (bit, nibble).bit4. A common definition for a word in computer jargon is a _____ (1, 16)-bit group of binary digits.16
24REVIEW Counting in Decimal and Binary Place Value Binary to Decimal ConversionDecimal to Binary ConversionElectronic TranslatorsHexadecimal NumbersOctal NumbersBits, Bytes and Words