In everyday life, the number system we use is base ten.<\/p>\n
The number 4062 means<\/p>\n
4×1000 + 0x100 + 6×10 + 2×1<\/p>\n
More specifically, it means<\/p>\n
4×103<\/span><\/sup>+0x102<\/span><\/sup>+6×101<\/span><\/sup>+2×100<\/span><\/sup><\/p>\n Recall, of course, that x0<\/span><\/sup>=1, x being any real number.<\/p>\n So, what is the number 57 in base 2?<\/p>\n Well, the powers of 2 are as as follows:<\/p>\n 20<\/span><\/sup>=1<\/p>\n 21<\/span><\/sup>=2<\/p>\n 22<\/span><\/sup>=2×2=4<\/p>\n 23<\/span><\/sup>=2x2x2=8<\/p>\n 24<\/span><\/sup>=2x2x2x2=16<\/p>\n 25<\/span><\/sup>=32<\/p>\n 26<\/span><\/sup>=64<\/p>\n and so on.<\/p>\n 57, written as a combination of powers of 2, can be thought of as<\/p>\n 1×32 + 1×16 + 1×8 + 0x4 + 0x2 + 1×1<\/p>\n or, in other words,<\/p>\n 1×25<\/span><\/sup> + 1×24<\/span><\/sup>+1×23<\/span><\/sup>+0x22<\/span><\/sup>+0x21<\/span><\/sup>+1×20<\/span><\/sup><\/p>\n Therefore, we have <\/p>\n 57=111001 in base 2.<\/p>\n Exercise: Verify that 129, when converted into base 5, is 1004.<\/strong><\/p>\n Solution: 129=1×125 + 0x25 + 0x5 + 4×1. Of course, 125=53<\/span><\/sup>, 25=52<\/span><\/sup>, and so on.<\/p>\n In computer science, the hexadecimal system – aka, base 16 – is often used. We’ll take a look at that in a future post:)<\/p>\n