I can't seem to comprehend a thing. I'm so incompetent at it. We're currently learning about bases such as base 2, base 8, base 10 etc...
I just don't understand it...Please help..and talk me through it and dumb it down for me, please.
I just don't understand it...Please help..and talk me through it and dumb it down for me, please.
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Note that in ordinary math we have the digits
0 1 2 3 4 5 6 7 8 9
after 9, we name the next integer ten
which we write as
10
placing a 1 in tens place and a zero in ones place
For different bases
10 denotes the number that is the base.
For example, in base 4
we count
1 2 3 then call the next digit
10 and write 10[base 4} so we will know
this is the number whose value is this many
☻☻☻☻
The next integer is then denoted
11[base 4] and has a value of 5 in base 10
the number 13[base 4] has value 4+3 = 7
the base 4 number after 13{base 4] is
20[base 4] = 2x 4 + 0 x 1 and it has a base 10 value of 8
If we have to take a base 4 number and convert it to base 10
for example 3102[base 4]
It would equal 3 x 4³ + 1 x 4² + 0 x 4¹ + 2 x 1
equals 3 x 64 + 16 + 0 + 2 = 192+ 16+ 2 = 210
The most common bases used in the computer world are 2,8 and 16
2 is very important because it uses digits 0 and 1 and that correponds to
electrical off and on so computers communicate with base 2 calculations.
The other name for base 2 is "binary" so you will often refer to binary
arithmetic.
You may also use hexadecimal, which means base 16.
Since there are only 9 basic digits,and 0 as a tenth we add 6 more to
create a total of 16, and we call those
a b c d e f
thus
a=10 and f=15 and
10[base 16] is equal to sixteen
the abbreviation h is often used
in place of [base 16] to denote a
hexadecimal numeral
so
11h = 17
and
20h = 32
a0h = 10x 16 = 160
0 1 2 3 4 5 6 7 8 9
after 9, we name the next integer ten
which we write as
10
placing a 1 in tens place and a zero in ones place
For different bases
10 denotes the number that is the base.
For example, in base 4
we count
1 2 3 then call the next digit
10 and write 10[base 4} so we will know
this is the number whose value is this many
☻☻☻☻
The next integer is then denoted
11[base 4] and has a value of 5 in base 10
the number 13[base 4] has value 4+3 = 7
the base 4 number after 13{base 4] is
20[base 4] = 2x 4 + 0 x 1 and it has a base 10 value of 8
If we have to take a base 4 number and convert it to base 10
for example 3102[base 4]
It would equal 3 x 4³ + 1 x 4² + 0 x 4¹ + 2 x 1
equals 3 x 64 + 16 + 0 + 2 = 192+ 16+ 2 = 210
The most common bases used in the computer world are 2,8 and 16
2 is very important because it uses digits 0 and 1 and that correponds to
electrical off and on so computers communicate with base 2 calculations.
The other name for base 2 is "binary" so you will often refer to binary
arithmetic.
You may also use hexadecimal, which means base 16.
Since there are only 9 basic digits,and 0 as a tenth we add 6 more to
create a total of 16, and we call those
a b c d e f
thus
a=10 and f=15 and
10[base 16] is equal to sixteen
the abbreviation h is often used
in place of [base 16] to denote a
hexadecimal numeral
so
11h = 17
and
20h = 32
a0h = 10x 16 = 160