Lesson 12 of 1524
Number representation
A number and the marks used to write it are different things.
Practice this chapterPlace value depends on the base. In base 10, each step left is worth ten times as much. In base 2, each step left is worth twice as much: 1, 2, 4, 8, and so on.
Hexadecimal is base 16. After 9, the digits continue A = 10, B = 11, up through F = 15.
A binary place
1101₂ = 1·8 + 1·4 + 0·2 + 1·1
Expand each digit by the power of the base underneath it.
Worked example
Convert 1101 in base 2 to base 10.
- 1From the right, the places are powers of 2: 1, 2, 4, and 8.
- 2The digits sit on those places: 1 is on 8, 1 is on 4, 0 is on 2, and 1 is on 1.
- 3A digit of 1 contributes that place value. A digit of 0 contributes nothing: 8, 4, 0, and 1.
- 4Add the contributions: 8 + 4 + 0 + 1 = 13.
Result: 13
Why. 1101₂ means one 8, one 4, no 2s, and one 1. Those are the only place values in the numeral, and they add to 13 in base 10.
The digit 2 cannot appear in a base-2 numeral. Only 0 and 1 are legal there.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.