Binary Number and bases

What base are normal numbers in?

What base are normal numbers in?

base 10 and the option of digits are 0-9

What does 0 and 1 mean in computers

0 = off

1 = on

what is a base

• A numbering system used to represent values

• the base is a numerical number represented in the subscript

• the option of digits is always 0 to n-1

• to convert the base multiply each digit by the baseⁿ starting from the ones digit where n = 0 and increases by one across the digits aka the tens digit n = 1 etc

• then add the products together to get the number in that base

What base do computers understand/work in

base 2

First method of converting to base 2

Quotient method of converting to base 2

• only pay attention to integers

• work right to left

• if the number is odd put a 1, if the number is even put a 0

• divide the original number wanting to be converted by 2, if the quotient is odd put a 1, if the number is even put a 0

  • only take the number, don’t round it and ignore the decimal

• continue till the quotient is 0, when the quotient is 0 the number is finished

Remainder method of converting to base 2

• only pay attention to integers

• work right to left

• if the number is odd put a 1, if the number is even put a 0

• divide the original number wanting to be converted by 2, put the quotient which is 0 or 1

  • only take the number, don’t round it and ignore the decimal

• continue till the quotient is 0

  • when the quotient is less than 1 multiply it byb the base and put it as 1

What is a more efficient way of converting bases with numbers of the same base but different powers

base 2 to base 8 = 2¹ to 2³ which means every 3 digits of the base 2 number is equal to 1 digit in base 8

(add 0s at the end when there are leftover digits)

what to write when number can’t be converted

error

what is hexidecimal code

base 16

How to represent digits >=10

use the alphabet starting from A=10, B=11, C=12, etc.

what is codemapping

mapping/assigning text to numbers

how are images made/stored

• made of pixels

• each pixel has a color and color is stored in binary

• for black and white, with 0s as black and 1s as white hence each pixel uses only 1 bit

• for color images each pixel has a range of 0-255 of r, g, and, b. each pixel needs 24 bits, each in base 2 but better to represent in base 16

  • #RRGGBB

Sign magnitude to store +/- numbers

• first digit shows whether they’re positive or negative,

  • 0 = positive

  • 1 = negative

• while the rest of the digits represent what the number was

• 11011= -11

1’s compliment to store +/- numbers

• first digit shows whether they’re positive or negative,

  • 0 = positive

  • 1 = negative

• flip the numbers i.e. every 0 becomes a 1 and vice versa

• find the value of the flipped number

• 11011 = -4

2’s compliment to store +/- numbers

• first digit shows whether they’re positive or negative,

  • 0 = positive

  • 1 = negative

• flip the numbers i.e. every 0 becomes a 1 and vice versa

• add 1, addition is done normally but all numbers done in binary

  • the 1 was added to fix the issue from previous methods where there was +/- 0s

• find the value of the new number

• 11011 = -5