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Atricle Dump - Coverting Decimal To 8-Bits Binary And Vice Versa
Journaling For Fun and Profit!
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Converting decimal to binary:
The rules are as follows:
*You should start from the left most binary digit
*If the decimal number is equal or greater than the place value (corresponding 2^number), then place the bit 1 and forward the difference to the next digit on the right
*If the decimal number is less than the place value , then place the bit 0 and forward the number as it is to the next digit on the right
Example:
Suppose you got the decimal number 170:
- 170 is greater than 128(2^7) , so the left most bit is 1 , get the difference 170-128=42
-forward 42 to the next digit
-42 is less than 64( 2^6), so place 0 and forward the number as it is (42) to the next step
-42 is greater than 32(2^5), so place 1 and forward the difference which is 42-32=10
-10 is less than 16(2^4), so place 0 and forward the 10 as it is
-10 is greater than 8(2^3) so place 1 and forward the difference which is 10-8=2
-2 is less than 4
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*If the decimal number is equal or greater than the place value (corresponding 2^number), then place the bit 1 and forward the difference to the next digit on the right
*If the decimal number is less than the place value , then place the bit 0 and forward the number as it is to the next digit on the right
Example:
Suppose you got the decimal number 170:
- 170 is greater than 128(2^7) , so the left most bit is 1 , get the difference 170-128=42
-forward 42 to the next digit
-42 is less than 64( 2^6), so place 0 and forward the number as it is (42) to the next step
-42 is greater than 32(2^5), so place 1 and forward the difference which is 42-32=10
-10 is less than 16(2^4), so place 0 and forward the 10 as it is
-10 is greater than 8(2^3) so place 1 and forward the difference which is 10-8=2
-2 is less than
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Example:
Suppose you got the decimal number 170:
- 170 is greater than 128(2^7) , so the left most bit is 1 , get the difference 170-128=42
-forward 42 to the next digit
-42 is less than 64( 2^6), so place 0 and forward the number as it is (42) to the next step
-42 is greater than 32(2^5), so place 1 and forward the difference which is 42-32=10
-10 is less than 16(2^4), so place 0 and forward the 10 as it is
-10 is greater than 8(2^3) so place 1 and forward the difference which is 10-8=2
-2 is less than
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-forward 42 to the next digit
-42 is less than 64( 2^6), so place 0 and forward the number as it is (42) to the next step
-42 is greater than 32(2^5), so place 1 and forward the difference which is 42-32=10
-10 is less than 16(2^4), so place 0 and forward the 10 as it is
-10 is greater than 8(2^3) so place 1 and forward the difference which is 10-8=2
-2 is less than
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-10 is less than 16(2^4), so place 0 and forward the 10 as it is
-10 is greater than 8(2^3) so place 1 and forward the difference which is 10-8=2
-2 is less than 4( 2^2) so place 0 and forward the 2 as it is
-2 is equal 2( 2^1) so place a 1 and forward the difference which is 2-2=0
-0 is less than 1(2^0) so place a zero and you're done
so the decimal number 170 is equal to the binary number 10101010
NOTE THE FOLLOWING:
*The right most place value is 2^0
*Whenever you get a zero difference, all the next digits will be o's as zero will be less than 2^whichever number
*Only numbers from 0-255 can be represented by 8 digits binary .Numbers greater than 255 will be represented by more bits. For example: 256 is represented by 9 digits: 100000000. In general 2^n -1 gives you the largest number that can be represented by n digits. So in 8 digits binary, max. number is 2^8 -1= 255. In 9 digits binary, max.number is 2^9-1=511. So the range for 9 digits is from 256-511. Starting from 512 ,10 digits will be required.And
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