How would we apply this
formula in decimal and binary? How many digits would it take to represent the value
123 in decimal and binary?
|
Decimal: |
|
Binary: |
|
|
I = |
10n |
I = |
2n |
|
log (I) = |
n
* log (10) |
log (I) = |
n
* log (2) |
|
= |
n * 1 |
= |
n * 0.30103 |
|
= |
n |
n = |
log(I)/0.30103 |
|
n = |
log (I) |
|
|
If we wished to represent the value
123, In Decimal and Binary, this would mean:
|
Decimal: |
|
Binary: |
|
|
123 = |
10n |
123 = |
2n |
|
log (123) = |
n
* log (10) |
log (123) = |
n
* log (2) |
|
= |
n * 1 |
= |
n * 0.30103 |
|
= |
n |
n = |
log(123)/0.30103 |
|
n = |
log (123) |
n = |
2.0899/0.30103 |
|
= |
2.0899 |
= |
6.9425 |
OR, you would need 2.0899
decimal digits or 6.9425 binary digits