Chapter 1 Flashcards
digital def
uses discrete physical states (ie high and low)
logic def
uses basic logic operations to interpret and process information
design def
to plan, analyze and construct the system that will fulfill the working requirements
analog
quantities measured continuously (wall clock)
digital (as in not analog)
quantities measured discretely
analog electronic system
accept and process continuous signals in the form of continuous voltage or current signals
digital electronic system
accept and process discrete samples that represent the actual continuous signal using an analog to digital converter
___ volts represents a logic 1 or logic high
+5
___ volts represents a logic 0 or logic low
0
advantages of digital system (6)
- storing and processing data is more efficient
- transmission of data is more efficient and reliable
- detecting and correcting error is easier
- data can be easily and precisely reproduced
- digital systems are easy to design and implement
- they require less space
Radix of a number
the base, each digit has a weight that is a power of the radix
a number system with radix r has how many allowed digits?
0, 1, … (r-1)
most significant digit
leftmost digit, has highest weight
least significant digit
rightmost digit, has lowest weight
what is the largest value that can be expressed in n digits in terms of the radix
r^n - 1
positional number system
each digit has a position that is associated with a fixed weight
bit
one binary digit
nibble
four bits
byte
eights bits
kilobyte
2^10
megabyte
2^20
gigabyte
2^30
terrabyte
2^40
Sum of weights method
multiply each binary digit with its fixed weight and add to get decimal value
Sum of non-zero terms
multiply each binary digit that is not one with its fixed weight and add to get
repeated division by 2 method
- to go from decimal to binary
- divide the decimal number repeatedly by 2, recording the remainder each time.
- the last remainder becomes the msb and the first remainder becomes the lsb
repeated multiplication by 2 method
- to go from decimal fractions to binary
- multiply the fraction part by the base (2)
- record the integer (0 or 1) then take the fraction part and multiply again
- repeat until no more fraction
- msb is the one recorded first, lsb is the one recorded last
Base-8
Octal, digits 0 - 7
base 16
hexadecimal, values 0-15, digits 0-F
binary to octal
started at lsb, take groups of 3 bits and convert each to decimal form to get octal representation
octal to binary
convert each octal digit into its 3bit form
decimal to octal (not fraction)
use repeated division by 8
binary to hexadecimal
group bits into groups of four starting with lsb, each group will represent one hexadecimal digit
hexadecimal to binary
each hexadecimal digit is replaced with the equivalent 4 bit string
decimal to hexadecimal
repeated division by 16
binary addition
similar to decimal, a sum bit and a carry bit are generated
4 possibilities for adding 2 bits together
basic binary subtraction
- results in a difference bit and a borrow bit
binary multiplication
- similar to decimal
- when multiplying 2 bits, product will be zero unless both bits are 1
binary division
- same procedure as decimal, may result in a remainder
signed binary numbers (or signed-magnitude representation)
msb is reserved to signify if number is positive (0) or negative (1)
unsigned binary numbers
assumed to be positive so msb is not reserved for the sign
diminished radix complement
- (r-1)’s complement
- for a number N with n digits, its complement is (r^n - 1) - N
1’s complement of a binary number
obtained by changing zero to one and one to zero
radix complement
- for a number N with n digits, its complement is (r^n - N)
- equivalent to one more than the diminished radix complement
2’s complement of a binary number
- add one to the 1’s complement
the msb of the 2’s complement of a negative number should be ____
1
subtraction by 2’s complement
- if any numbers are negative, take 2’s complement (msb should be 1, so msb doesn’t change from signed magnitude to complement)
- then take 2’s complement of the subtrahend including the sign bit
- if there is a carry out bit, ignore it
- then add the two numbers
an n-bit binary code can have up to ____ distinct combinations of 1’s and 0’s
2^n
BCD
- binary coded decimal
- used for applying a decimal input to a digital circuit
- each decimal digit is represented by 4 bits that can go up to a max value of 9 (1001) (other values are dont care on k map)
BCD addition
- if binary sum is equal to or less than 1001, BCD digit is correct
- if binary sum is more than 1001, add 6 to it to get the correct digit and carry
ASCII code
- american standard code for information interchange
- uses 7 bits to code 128 characters
- includes uppercase, lowercase, punctuation, numbers 0-9, and some nonprinting characters for control functions
parity bit
a bit added to the front of the code to make there an odd or even number of bits to check correctness of code
