Converting 37, 65, 350, 427 to binary can be done by figuring out what power of two is the largest that fits into the number, noting that value in binary, subtracting the value from the number, and repeating until the number is zero.
Converting 37 to binary: 32 (100000b) is the greatest power of two <= 37. Number is now 37 - 32, which equals 5. 4 (100b) is the greatest power of two <= 5. Number is now 5 - 4, which equals 1. 1 (1b) is the greatest power of two <= 1. Number is now 1 - 1, which equals 0. Summing the powers of two that we found, we find that 37 in binary is 100000b + 100b + 1b = 100101b.
Converting 65 to binary: 64 (1000000b) is the greatest power of two <= 65. Number is now 65 - 64, which is 1. 1 (1b) is the greatest power of two <= 1. Number is now 1 - 1, which equals 0. Summing the powers of two that we found, we find that 65 in binary is: 1000000b + 1b = 1000001b.
Converting 350 to binary: 256 (100000000b) is the greatest power of two <= 350. Number is now 350 - 256, which is 94. 64 (1000000b) is the greatest power of two <= 94. Number is now 94 - 64, which is 30. 16 (10000b) is the greatest power of two <= 30. Number is now 30 - 16, which is 14. 8 (1000b) is the greatest power of two <= 14. Number is now 14 - 8, which is 6. 4 (100b) is the greatest power of two <= 6. Number is now 6 - 4, which is 2. 2 (10b) is the greatest power of two <= 2. Number is now 2 - 2, which equals 0. Summing the powers of two that we found, we find that 350 in binary is: 100000000b + 1000000b + 1000b + 100b + 10b = 101001110b.
Converting 427 to binary: 256 (100000000b) is the greatest power of two <= 427. Number is now 427 - 256, which is 171. 128 (10000000b) is the greatest power of two <= 171. Number is now 171 - 128, which is 43. 32 (100000b) is the greatest power of two <= 43. Number is now 43 - 32, which is 11. 8 (1000b) is the greatest power of two <= 11. Number is now 11 - 8, which is 3. 2 (10b) is the greatest power of two <= 3. Number is now 3 - 2, which is 1. 1 (1b) is the greatest power of two <= 1. Number is 1 - 1, which equals 0. Summing the powers of two that we found, we find that 427 in binary is: 100000000b + 10000000b + 100000b + 1000b + 10b + 1b = 110101011b.