Answer:
(a) 1001 base 2 = <u>9</u> base 10
(b) 1101 base 2 = <u>13</u> base 10
Basically, 9 and 13.
Step-by-step explanation:
Follow the chart of the binary system:
2n...
2^4 2^3 2^2 2^1 2^0
sixteens eights fours twos ones
Put one number onto each place, starting from the right side. Since there are 5 places of 2 to the power of something, and 1001 is only 4 numbers, you'll have an extra 0. So...
2n... 0 1 0 0 1
2^4 2^3 2^2 2^1 2^0
sixteens eights fours twos ones
Now that you've placed the numbers, you now know there's one 2^3 which is 1 multiplied by 2^3 = 8 (it is eight because under 2^3, it says eights) and 1 2^0 which is 1 multiplied by 2^0 which is 1 (because under 2^0 it says ones).
Add 8 and 1. 8 + 1 = 9
9 is the decimal number for 1001.
Do the same from 1101, put the numbers above their places in the chart, see how much 2^? are there, then add its place values to get the answer.
2n... 0 1 1 0 1
2^4 2^3 2^2 2^1 2^0
sixteens eights fours twos ones
1 multiplied by 2^3 = 8, 1 multiplied by 2^2 = 4, 1 multiplied by 2^0 = 1.
8 + 4 + 1 = 13
13 is the decimal number for 1101.
I hope this helps!! I'm about to be a sophomore this year and I had the same question..!
