Chap 1 - Data representation (no. systems, [text, sound, video, image], [data storage and file compression]) Flashcards
name the number systems
-binary
-hexadecimal
-Octal
-denary
note: sequence for 2 powers starts form 1
what are the bases for the number systems
-binary - 2
-hexadecimal -16
-Octal - 8
-denary- 10
numbers in Hexadecimal
0 to F
numbers in octal
0 - 7
numbers in denary
0 - 9
numbers in binary
0 - 1
what does 1 mean in binary
- ON, TRUE, HIGH
- flow of electrical signals
what does 0 mean in binary
- OFF, FALSE, LOW
- absence of flow of electrical signals
sequence for binary until 2^13
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192
what are numbers in binary called
bit
what is Least significant bit (LSB)
bit on the extreme right
what is Most significant bit (MSB)
bit on the extreme left
what is assigned to each bit
index value
what does index value start and end with
0 until MSB in denary
how do you go binary to denary
- use sequence
- multiply the 1 bit by 2 to the power of its index value. and add values
eg, 101 - 1x2^0 + 1x2^2 = 5
how do you go denary to binary
-divide number by 2 until you get 0
-track remainders and take from bottom to top
eg, 2| 12 0
2| 6 0
2| 3 1
2|1
0
9 = 1100
-bottom will be MSB
how do you go from binary to hexadecimal
-group bits into groups of 4 starting from LSB
-add 00 at MSB to complete groups
-convert each group to hexadecimal
-write the numbers starting from MSB group
eg. 0001 1010 = 1A
1 A (hexadecimal)
-MSB no. will start
how do you go binary to ocotal
-group bits into groups of 3 starting from LSB
-add 00 at MSB to complete groups
-convert each group to denary
-write the numbers starting from MSB group
eg. 001 010 = 12 - octal
1 2 (denary)
-MSB no. will start
how do you go from octal to binary
-write the binary bits for each octal digit
how do you go from hexadecimal to binary
-write the binary bits for each hex digit
the bits for hex 9 - F
hex - binary - denary
9 - 1001 |9
A - 1010 |10
B - 1011 |11
C - 1100 |12
D - 1101 |13
E - 1110 |14
F - 1111 |15
number systems conversion algorithms
Hex
|
Octal - Binary - Denary
H - B - 1 digit = 4 bits
O - B - 1 digit = 3 bits
D - B - divide by 2
B - D - sequence
why is binary used in computers
-computers are made up of logic gates
-which only have 2 states (0 or 1)