Signals and Number Systems
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Analog Signals
Digital Signals
Number System
Complement and Two's Complement
Binary-Coded Decimal (BCD)
Coding Schemes
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Signal is information converted into electric form suitable for transmission
Signal is used to carry data from one device or network to another
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Analog Signals have amplitude that changes gradually over time
Analog Signals can be periodic or nonperiodic
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Characteristics of an Analog Signal:
Frequency
Amplitude
Phase
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Units of Frequency and Period
Frequency is the number of cycles in 1 second (Hz)
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Amplitude refers to the magnitude or strength of an analog signal
Phase is the position of a wave at a point in time on a waveform cycle
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Digital Signals are discrete in terms of time
Digital Signals portray data and information as a series of distinct values
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Number Systems are used to express numbers in various forms understood by computers
Types of Number Systems: Decimal, Binary, Octal, Hexadecimal
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Decimal Number System is base 10 and associates with 10 digits (0-9)
Binary Number System is base 2 and associates with 2 digits (0 and 1)
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Octal Number System is base 8 and associates with 8 digits (0-7)
Hexadecimal Number System is base 16 and associates with 16 digits/alphabets (0-9, A-F)
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Converting Binary to Decimal:
Write down the binary number
Assign positional values to each digit
Multiply each binary digit with its positional value
Add all the results to get the decimal equivalent
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Converting Binary to Octal:
Group binary digits into sets of three
Write down the octal equivalent of each group
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Converting Binary to Hexadecimal:
Group binary digits into sets of four
Write down the hexadecimal equivalent of each group
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Converting Octal to Decimal:
Write down the octal number
Assign positional values to each digit
Multiply each octal digit with its positional value
Add all the results to get the decimal equivalent
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Converting Octal to Binary:
Write down the octal number
Replace each octal digit with its binary equivalent
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Converting Decimal to Binary:
Group binary digits into sets of four
Write down the hexadecimal equivalent of each group
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1's complement and 2's complement are types of complements for binary numbers
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To get 1's complement of a binary number, invert the given bits or numbers
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Example of representing +6 and -6 in 5-bit binary
+6 is represented as 00110
1's complement of 00110 is 11001
Sign bit determines if the number is positive or negative
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To get 2's complement of a binary number, invert the given number and add 1 to the LSB
Example: 2's complement of binary number 10101110 is 01010010
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Example of representing -28 in 8-bit binary
Write out +28 in binary form: 00011100
Invert each bit: 11100011
Add 1 to the LSB: 11100100
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Binary-Coded Decimal (BCD) is a binary representation of decimal digits
Each decimal digit is represented by a set of four binary digits or bits
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BCD representation of digits 0 to 9
BCD is achieved through complements (1's & 2's), binary arithmetic (addition), and positional weights
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Positional weights for converting decimal to BCD
Rightmost bit has a weight of 1
Second bit from the right has a weight of 2
Third bit from the right has a weight of 4
Leftmost bit has a weight of 8
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Example of converting decimal number 237 to BCD
BCD representation: 0010 0011 0111 (packed BCD)
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Example of converting BCD to decimal number
BCD representation: 110010
Decimal number: ? ? 1 1 0 0 1 0 1
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ASCII CODE is a standardized method for representing and encoding data
Essential for accurate interpretation and processing of data by computers and digital devices
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ASCII Code is a seven (7) bit code
It has 128 bit patterns
It can represent 256 characters
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ASCII Code types: Control Characters and Printable Characters
Control Characters are non-printable (e.g., Tab, Enter)
Printable Characters include numbers, symbols, capital letters, and small letters
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ASCII Code table showing decimal, binary, hexadecimal, and ASCII values for characters
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ASCII Code table continuation showing decimal, binary, hexadecimal, and ASCII values for characters
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ASCII codes for characters from 74 to 111
Details:
Character: 74, Binary: 0100 1010, Hexadecimal: 4A, ASCII: J
Character: 93, Binary: 0101 1101, Hexadecimal: 5D, ASCII: ]
Character: 75, Binary: 0100 1011, Hexadecimal: 4B, ASCII: K
Character: 94, Binary: 0101 1110, Hexadecimal: 5E, ASCII: ^
Character: 76, Binary: 0100 1100, Hexadecimal: 4C, ASCII: L
Character: 95, Binary: 0101 1111, Hexadecimal: 5F, ASCII: -
Character: 77, Binary: 0100 1101, Hexadecimal: 4D, ASCII: M
Character: 96, Binary: 0110 0000, Hexadecimal: 60, ASCII: I
Character: 78, Binary: 0100 1110, Hexadecimal: 4E, ASCII: N
Character: 97, Binary: 0110 0001, Hexadecimal: 61, ASCII: a
Character: 79, Binary: 0100 1111, Hexadecimal: 4F, ASCII: O
Character: 98, Binary: 0110 0010, Hexadecimal: 62, ASCII: b
Character: 80, Binary: 0101 0000, Hexadecimal: 50, ASCII: P
Character: 99, Binary: 0110 0011, Hexadecimal: 63, ASCII: C
Character: 81, Binary: 0101 0001, Hexadecimal: 51, ASCII: Q
Character: 100, Binary: 0110 0100, Hexadecimal: 64, ASCII: d
Character: 82, Binary: 0101 0010, Hexadecimal: 52, ASCII: R
Character: 101, Binary: 0110 0101, Hexadecimal: 65, ASCII: e
Character: 83, Binary: 0101 0011, Hexadecimal: 53, ASCII: S
Character: 102, Binary: 0110 0110, Hexadecimal: 66, ASCII: f
Character: 84, Binary: 0101 0100, Hexadecimal: 54, ASCII: T
Character: 103, Binary: 0110 0111, Hexadecimal: 67, ASCII: g
Character: 85, Binary: 0101 0101, Hexadecimal: 55, ASCII: U
Character: 104, Binary: 0110 1000, Hexadecimal: 68, ASCII: h
Character: 86, Binary: 0101 0110, Hexadecimal: 56, ASCII: V
Character: 105, Binary: 0110 1001, Hexadecimal: 69, ASCII: i
Character: 87, Binary: 0101 0111, Hexadecimal: 57, ASCII: W
Character: 106, Binary: 0110 1010, Hexadecimal: 6A, ASCII: j
Character: 88, Binary: 0101 1000, Hexadecimal: 58, ASCII: X
Character: 107, Binary: 0110 1011, Hexadecimal: 6B, ASCII: k
Character: 89, Binary: 0101 1001, Hexadecimal: 59, ASCII: Y
Character: 108, Binary: 0110 1100, Hexadecimal: 6C, ASCII: I
Character: 90, Binary: 0101 1010, Hexadecimal: 5A, ASCII: Z
Character: 109, Binary: 0110 1101, Hexadecimal: 6D, ASCII: m
Character: 91, Binary: 0101 1011, Hexadecimal: 5B, ASCII: [
Character: 110, Binary: 0110 1110, Hexadecimal: 6E, ASCII: n
Character: 92, Binary: 0101 1100, Hexadecimal: 5C, ASCII: \
Character: 111, Binary: 0110 1111, Hexadecimal: 6F, ASCII: o
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ASCII codes for characters from 112 to 127
Details:
Character: 112, Binary: 0111 0000, Hexadecimal: 70, ASCII: p
Character: 113, Binary: 0111 0001, Hexadecimal: 71, ASCII: q
Character: 114, Binary: 0111 0010, Hexadecimal: 72, ASCII: r
Character: 115, Binary: 0111 0011, Hexadecimal: 73, ASCII: S
Character: 116, Binary: 0111 0100, Hexadecimal: 74, ASCII: t
Character: 117, Binary: 0111 0101, Hexadecimal: 75, ASCII: u
Character: 118, Binary: 0111 0110, Hexadecimal: 76, ASCII: V
Character: 119, Binary: 0111 0111, Hexadecimal: 77, ASCII: W
Character: 120, Binary: 0111 1000, Hexadecimal: 78, ASCII: X
Character: 121, Binary: 0111 1001, Hexadecimal: 79, ASCII: y
Character: 122, Binary: 0111 1010, Hexadecimal: 7A, ASCII: Z
Character: 123, Binary: 0111 1011, Hexadecimal: 7B, ASCII: {
Character: 124, Binary: 0111 1100, Hexadecimal: 7C, ASCII: I Vertical bar
Character: 125, Binary: 0111 1101, Hexadecimal: 7D, ASCII: }
Character: 126, Binary: 0111 1110, Hexadecimal: 7E, ASCII: 2 Tilde
Character: 127, Binary: 0111 1111, Hexadecimal: 7F, ASCII: DEL Delete
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Decimal, Hexadecimal, Binary, and ASCII codes for characters
Details:
Decimal: 77, Hexadecimal: 4D, Binary: 01001101, ASCII: M
Decimal: 91, Hexadecimal: 5B, Binary: 01011011, ASCII: [
Decimal: 104, Hexadecimal: 68, Binary: 01101000, ASCII: h
Decimal: 84, Hexadecimal: 54, Binary: 01010100, ASCII: T
Decimal: 54, Hexadecimal: 36, Binary: 00110110, ASCII: 6
Decimal: 32, Hexadecimal: 20, Binary: 00100000, ASCII: Space
Decimal: 16, Hexadecimal: 10, Binary: 00010000, ASCII:
Decimal: 8, Hexadecimal: 08, Binary: 00001000, ASCII:
Decimal: 4, Hexadecimal: 04, Binary: 00000100, ASCII:
Decimal: 2, Hexadecimal: 02, Binary: 00000010, ASCII:
Decimal: 1, Hexadecimal: 01, Binary: 00000001, ASCII:
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Decimal, Binary, and ASCII codes for characters
Details:
Decimal: 68, Binary: 01000100, ASCII: D
Decimal: 64, Binary: 01000000, ASCII: @
Decimal: 32, Binary: 00100000, ASCII: Space
Decimal: 16, Binary: 00010000, ASCII:
Decimal: 8, Binary: 00001000, ASCII:
Decimal: 4, Binary: 00000100, ASCII:
Decimal: 2, Binary: 00000010, ASCII:
Decimal: 1, Binary: 00000001, ASCII:
Decimal: 65, Binary: 01000001, ASCII: A
Decimal: 84, Binary: 01010100, ASCII: T
Decimal: 65, Binary: 01000001, ASCII: A
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Decimal, Hexadecimal, Binary, and ASCII codes for characters
Details:
Decimal: 68, Hex