A. can you think of a situation where it would make the most sense to express your birth year in binary numbers? b. hexadecimal numbers? c. decimal numbers?

We usually express our birth year in Decimal numbers. That is, if the birth year is 2000, then we write 2000 as 2000 itself in decimal numbers. This is because we use decimal number system in our daily life.

But we can express any decimal number as binary or hexadecimal numbers too.

Let the birth year we consider be 2000.

(a) We need to find the binary numbers for 2000. We say Binary numbers as the numbers in base 2. Binary numbers consist of 0 and 1 only as digits.

So in order to find the binary representation we divide 2000 by 2 and write down the remainder. Then we again divide the above quotient by 2 and note down the remainder again. We continue this process until we divide the last quotient by 2 and find the remainder. Then the remainders written in the reverse order gives the binary number for 2000.

That is,

2000 = 2 x 1000 + 0

1000 = 2 x 500 + 0

500 = 2 x 250 + 0

250 = 2 x 125 + 0

125 = 2 x 62 + 1

62 = 2 x 31 + 0

31 = 2 x 15 + 1

15 = 2 x 7 + 1

7 = 2 x 3 +1

3 = 2 x 1 + 1

1 = 2 x 0 + 1

Writing the remainders from bottom to top , we get,

11111010000 is the binary expression for 2000.

(b) Hexadecimal number system consist of 16 digits : 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F, where A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

Now we use the same above process with 2 replaced by 16.

That is,

2000 = 16 x 125 + 0

125 = 16 x 7 + 13

7 = 0 x 16 + 7

Writing down the remainders from bottom to top, we get,

7D0 (Here D represents 13 in hexadecimal number system).

(c) The Decimal number system consists of the digits: 0,1,2,3,4,5,6,7,8,9

So 2000 is originally expressed in the decimal number system itself.

Learn more about the Number systems at https://brainly.com/question/21751836

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