Number Systems Flashcards
how do digital systems differ from analogue quantities
digital systems can process, store and transmit data more efficiently
- they also can only assign discrete values to each point
What are the 2 states of digital electronics (voltage/logic levels)
HIGH or LOW
What discrete values are assigned in digital systems
1 binary - HIGH
0 binary - LOW
what is a digital waveform
a series of pulses
- change between LOW and HIGH levels
What is a positive-going pulse
a digital waveform that goes from a normally low logic level to a high logic level, before returning to a low logic level
what is a negative-going pulse
a digital waveform that goes from a normally high logic level to a low logic level, before returning to a high logic level
what is a duty cycle
the ratio of pulse width (tw) to wave period (T)
how is duty cycle calculated
(tw/T) x 100%
tw - pulse width
T - period (time for full cycle)
what is high duty cycle
a waveform that is high most of the time
what is a low duty cycle
a waveform that is low most of the time / high for a short amount of time
what are periodic pulse waveforms
pulses that repeat in a fixed interval (period)
what is frequency
the rate the periods of a wave repeats
how is frequency calculated
1/ T
T - period
what is a clock
a timing reference signal that synchronises basic timing waveforms with all waveforms
- interval between pulses = time for one bit of data
what is a timing diagram
a graph of digital waveforms showing the actual time relationship of 2 or more waveforms & how each waveform changes in relation to the other
how many bits are in a byte
8
how many bytes are in a word
2
how many bytes are in a double word
4
how can data be transmitted
serial transfer or parallel transfer
what is serial transfer/transmission
serial transfer of 8 bits of binary data, starting at interval t0-t1
- 1 bit at a time consecutively in intervals
what is parallel transfer/transmission
parallel transfer of 8 bits of binary data, starting at t0
- faster than series transmission
- delivers multiple bits as a single unit
how do binary systems work for digital systems
uses bases of 2 (2^n)
how to convert decimal to binary
keep dividing the decimal number by 2 and write down the remainders
how to convert decimal fraction to binary
repeatedly multiply fractional (< 0) results by 2 and carry the binary number at the front
rules for binary addition
0+0 = 0 (carry 0)
0+1 = 1 (carry 0)
1+0 = 1 (carry 0)
1 + 1= 0 (carry 1)
if 1 is carried:
1+0+0 = 01 sum:1 carry: 0
1+0+1 = 10. sum: 0 carry: 1
1+1+0 = 10. sum: 0 carry: 1
1+1 + 1= 11 sum: 1 carry: 1
binary rules for subtraction
0-0 = 0
0-1 = 1
1-0 = 1
1-1 = 0
what is the 1’s complement of a binary numbers
inverse of the digits
1 becomes 0
0 becomes 1
what are the 2’s complement of a binary number
adding 1 to the binary number
what is a signed binary number
they. indicates whether a number is positive or negative, and the magnitude is the value of
the number
Positive numbers in 2’s complement form are stored in true form (with a 0 for the sign
bit)
negative numbers are stored in complement form (with a 1 for the sign bit).
what are Hexadecimal numbers
sixteen characters to represent numbers: the numbers 0
through 9 and the alphabetic characters A through F
