Demonstrate your knowledge of converting a decimal number into binary by taking

Question

Demonstrate your knowledge of converting a decimal number into binary by taking any decimal number between 2500 and 7500. Then when done and to prove that you did it correctly, convert the binary number back to decimal. You must show all work. When done convert your binary number into hex. If you would prefer doing this conversion in hex rather than binary to mix it up, go for it. I do NOT want you to use a calculator that does the conversion automatically for you. Provide an explanation of how you did it. No 2 classmates should choose the same number, please vary the numbers. For example, I don't want one person choosing 2500 and another classmate choosing that same number. Ideally, I don't want you to use a number that is relatively close to another classmates. For example, if one student chooses 2500 don't choose 2501. I would prefer the second person choose something like 3432. Again these are only examples. This discussion board should help you through the Number Conversion Worksheet that you have to do for this weeks homework, and I would anticipate a test question on this as well. Please only 1 post/person unless you are helping or responding to a fellow classmate. By looking at the binary number is there an easy way to determine whether or not the binary number is even or odd? If there is, please describe

Explanation / Answer

suppose we are given a decimal number X and we need to convert it into binary number;

=> we divide the number by 2 each time until the number becomes 0 and save the remainder at each stage;

suppose X = 11;
=> 11/2 = 5; remainder = 1;
=> 5/2 = 2; remainder = 0;
=> 2/2 = 1; remainder = 1;
=> 1/2 = 0; remainder = 1;

decimal(11) = binary(1101);

suppose X = 21
=> 21/2 = 10; remainder = 1;
=> 10/2 = 5; remainder = 0;
=> 5/2 = 2; remainder = 0;
=> 2/2 = 1; remainder = 1;
=> 1/2 = 0; remainder = 1;

decimal(21) = binary(11001);

for convert decimal into hexadecimal, we need to divide by 16;
if remainder is 10, a is used;
if remainder is 11, b is used;
if remainder is 12, c is used;
if remainder is 13, d is used;
if remainder is 14, e is used;
if remainder is 15, f is used;

suppose X = 65;
=> 79/16 = 4; remainder = 15;
=> 4/2 = 0; remainder = 4;

decimal(65) = hexadecimal(4f);

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