Conversion Between Binary And Decimal
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Conversion between Binary and Decimal Generally logical 0 represents a potential difference of 0V In the same manner logical 1 represents 5V Logical 0 occurs when current cannot flow (e.g. through an open switch) Logical 1 occurs when current can flow (e.g. through a closed switch) and there is some current being supplied (e.g. from the Vcc pin on Integrated Circuits)
Binary Notation Binary numbers are in base 2. This is because each digit can only be one of 2 numbers, i.e. 0 or 1. Decimal numbers (the ones we most commonly use) are in base 10. Each digit can be either 0,1,2,3,4,5,6,7,8, or 9. Binary numbers are represented with a % prefix or a 2 subscripted suffix. Decimal numbers can have a 10 subscripted suffix. (This means that there is a little 10 after the number!)
Conversion from Binary to Decimal If you want to make life easy for yourself get a calculator which can work in different bases! In Decimal we are used to thinking about numbers as a combination of Units, Tens, Hundreds, etc. 107 1000000 0
106 100000 0
105 10000 0
104 103 102 1000 1000 100 0
101
100
10
1
For Example: 1652 (base 10) = 1 Thousand + 6 Hundreds +5 Tens + 2 Units. 1
In Binary we can think of numbers as a combination of Ones, Twos, Fours, Eights, Sixteen's, etc. 27 128
26 64
25 32
24 16
23 8
22 4
21 2
20 1
Similarly: %10110 (base 2) = 1 sixteen + 1 four + 1 two = 22 (in base 10) Or: %1100101 = 1 sixty-four + 1 Thirty-two + 1 four + 1 one = 10110 27 128
26 64 1 64
25 32 1 +32
24 16 0 +0
23 8 0 +0
22 4 1 +4
21 2 0 +0
20 1 1 +1
=10110
So: 11001012 = 10110 Conversion from Decimal to Binary Divide the number repeatedly by 2 (Answer being a whole number and a remainder, The same as Modula-2 Div and Mod commands) The First remainder is the LSB (Least Significant Bit or Digit, the digit on the right of the number) of the Binary number. The next remainder is the next digit, and so on until the value is 0. For Example: Convert 145 into base 2. 145/2= 72 r 1 72/2= 36 r 0 36/2= 18 r 0 18/2= 9 r0 9/2= 4 r1 4/2= 2 r0 2/2= 1 r0 2
1/2= 0 So: 14510 = %10010001
r1
3
Binary Notation Binary numbers are in base 2. This is because each digit can only be one of 2 numbers, i.e. 0 or 1. Decimal numbers (the ones we most commonly use) are in base 10. Each digit can be either 0,1,2,3,4,5,6,7,8, or 9. Binary numbers are represented with a % prefix or a 2 subscripted suffix. Decimal numbers can have a 10 subscripted suffix. (This means that there is a little 10 after the number!)
Conversion from Binary to Decimal If you want to make life easy for yourself get a calculator which can work in different bases! In Decimal we are used to thinking about numbers as a combination of Units, Tens, Hundreds, etc. 107 1000000 0
106 100000 0
105 10000 0
104 103 102 1000 1000 100 0
101
100
10
1
For Example: 1652 (base 10) = 1 Thousand + 6 Hundreds +5 Tens + 2 Units. 1
In Binary we can think of numbers as a combination of Ones, Twos, Fours, Eights, Sixteen's, etc. 27 128
26 64
25 32
24 16
23 8
22 4
21 2
20 1
Similarly: %10110 (base 2) = 1 sixteen + 1 four + 1 two = 22 (in base 10) Or: %1100101 = 1 sixty-four + 1 Thirty-two + 1 four + 1 one = 10110 27 128
26 64 1 64
25 32 1 +32
24 16 0 +0
23 8 0 +0
22 4 1 +4
21 2 0 +0
20 1 1 +1
=10110
So: 11001012 = 10110 Conversion from Decimal to Binary Divide the number repeatedly by 2 (Answer being a whole number and a remainder, The same as Modula-2 Div and Mod commands) The First remainder is the LSB (Least Significant Bit or Digit, the digit on the right of the number) of the Binary number. The next remainder is the next digit, and so on until the value is 0. For Example: Convert 145 into base 2. 145/2= 72 r 1 72/2= 36 r 0 36/2= 18 r 0 18/2= 9 r0 9/2= 4 r1 4/2= 2 r0 2/2= 1 r0 2
1/2= 0 So: 14510 = %10010001
r1
3
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