Perform the following conversions and operations, do not use the calculator. Show allyour work to receive full marks.a. Convert the decimal number 75 to binary

Sure, here's how you convert the decimal number 75 to binary:

Step 1: Start with the number 75. The largest power of 2 less than 75 is 64 (which is 2^6). So, write down "1" for 2^6. Now, subtract 64 from 75, which gives you 11.

Step 2: The largest power of 2 less than 11 is 8 (which is 2^3). So, write down "1" for 2^3. Now, subtract 8 from 11, which gives you 3.

Step 3: The largest power of 2 less than 3 is 2 (which is 2^1). So, write down "1" for 2^1. Now, subtract 2 from 3, which gives you 1.

Step 4: The largest power of 2 less than or equal to 1 is 1 (which is 2^0). So, write down "1" for 2^0. Now, subtract 1 from 1, which gives you 0.

Step 5: Fill in the remaining powers of 2 with "0" where necessary. In this case, for 2^2, 2^4 and 2^5.

So, the binary representation of the decimal number 75 is 1001011.