a. | The answer is 100110. The highest power of 2 we can make with 38 is 32, so our columns should read 32, 16, 8, 4, 2, and 1. We can use the 32 (38 - 32 = 6), so we record a 1 in that column. We can't use a 16 or an 8, so we record zeros in those columns. The next-highest power we can use is 4 (6 - 4 = 2), so we record a 1 in that column as well as the next one. Therefore, 38ten = 100110two. |
b. | The answer is 111111. The highest power we can make with 63 is 32, so our columns should read 32, 16, 8, 4, 2, and 1, as before. We can use the 32 (63 - 32 = 31), so we record a 1 in that column. We can use the next-highest power, 16 (31 - 16 = 15), then the next-highest (15 - 8 = 7), then the next-highest (7 - 4 = 3), then the next-highest (3 - 2 = 1), and finally the last power (1 - 1 = 0). All six columns are filled with 1s, so 63ten = 111111two. |
