Data representation - Number systems (paper 1) Flashcards
what is the order of binary representation
Bit, Nibble, Byte, Kibibyte, Mebibyte, Gigabyte, Tebibyte, Pebibyte, Exibyte
Ben Nibbled Bens Keish Made Gratefully To Paul
how and why do computers use binary to represent all forms of data
- computers are made up of switches : 2 states= off (0) and on (1)
- all data needed to be converted into binary to be processed by computer
- data is processed using logic gates and stored in registers
how many bits are in a Nibble
4
how many bits are in a Byte
8
how many bytes are in Kibibyte
1024 bytes
how many KiB are in a MiB
1024 KiB
how to convert binary into positive denary
- write out the place holders above the binary - 1,2,4,8,16….
- add the numbers which have a 1 under
what base system does denary have
base of 10
how to convert positive denary into binary
- start with the most significant bit
- then keep going down
what number system does hexadecimal have
base 16
what are 10 - 15 represented by in hexadecimal
A-F
how to convert binary into hex
- split 8-bit binary number into 2 nibbles of 4 bits
- convert each nibble separately - starting from 1,2,4,8
convert 01001111 into hex
0100 = 4
1111 = 15 = F
4F
how convert hex into binary
- convert each hex value into a 4-bit binary value
- join to make a byte
convert 7E into binary
7 = 0111
E = 14 = 1110
01111110
how to convert hex into denary
- multiply hex digits by their column place values 16 and 1
- add results**
convert 5B into denary
5 x 16 = 80
B = 11
11 x 1 = 11
80 + 11 = 91
how to convert denary into hex
- work out how many 16 go into the number = 1st hex digit
- take remainder = 2nd hex digit
convert 219 into hex
219 / 16 = 13 r 11
13 = D
11 = B
DB
how and why hexadecimal is used as a beneficial method of data representation.
- hex is easier to humas to read + remember than binary - shorter representation than binary
2 main uses
what are the 4 uses of hex within areas of computer science
- Colour values in photo editing + web design –> 1Hex no. = 1 nibble
- MAC addresses = unique number given to all Internet-connected devices - each address written in hex
- IPv6 addresses
- Unicode
what are the rules of binary addition
0+0 = 1
0+1 = 1
1+1 = 0 carry 1
1+1+1 = 1 carry 1
add 01011011 + 00111010
01011011
00111010
——————-
10010101
when will an overflow occur
- occurs when the result of adding 2 binary numbers is greater than the bits allowed:
- max value in a 8-bit register = 255
- a computer or a device has a predefined limit
that it can represent or store, e.g. 16-bit
Effect of right logical shifts:
x2 each time
what is the effect of shifting to the right
divide by 2 each time
what happens binary shifts and what happens in the empty spaces when the binary is shifted
- The positive binary integer is multiplied or
divided according to the shift performed - The most significant bit(s) or least significant
bit(s) are lost - Bits shifted from the end of the register are lost
and zeros are shifted in at the opposite end of the
register
when does an issue occur regarding the precision in binary shifts
- when odd numbers are divided / numbers that can fully divide –> byte cannot represent fractional numbers
- when 1 is lost at the end = last digit dropped is odd
what is the meaning of unsigned and signed representation
Unsigned = binary number can only represent positive numbers
Signed = represent both positive + negative numbers
in twos complement what does the left most bit represent
it is the sign bit:
- 1 = negative
- 0 = positive
what is the maximum and minimum value a signed 8-bit register can hold
max = 127
min = -128
what number is the leftmost bit in binary two’s complement if the number is negative
1
how to convert negative denary number into binary
- work out positive binary equivalent
- flip all bits
- add 1
convert -21 into binary
21 = 0001 0101
flip = 1110 1010
+1 = ____________1
convert:1110 1011
how do you convert negative twos complement binary number to denary
- flip
- add 1
- work it positive denary
- switch it to the negative equivalent
