Final answer:
To convert denary numbers to binary, divide by 2 and note the remainders, which form the binary number when read in reverse order. The binary equivalents for the given numbers are: 36 (100100), 137 (10001001), 254 (11111110), 184 (10111000), 212 (11010100), and 500 (111110100).
Step-by-step explanation:
Converting denary numbers (also known as decimal or base-10 numbers) into binary numbers (base-2) involves dividing the number by 2 and keeping track of the remainders, which will form the binary number. Let's work through the conversions for the provided numbers:
- 36 in binary: Divide 36 by 2 to get 18 with a remainder of 0, and continue dividing the quotient by 2 and noting the remainders until the quotient is 0. The binary number for 36 is 100100.
- 137 in binary: Repeating the same process, we get the binary number for 137 as 10001001.
- 254 in binary: Following the process, the binary number for 254 is 11111110.
- 184 in binary: The binary number for 184 is 10111000.
- 212 in binary: The binary number for 212 is 11010100.
- 500 in binary: Finally, the binary number for 500 is 111110100.
Each division step involves taking the current quotient, dividing by 2, and noting the remainder until we get a quotient of zero. The binary number is read by listing the remainders in reverse order, from the last division step back to the first.