CPSC 110-08: Computing on Mobile Phones Spring 2012 Homework: Powers of Two Due: Friday 2/3 (before class)

CS Principles

• 5: The student can describe the combination of abstractions used to represent data.
• 6: The student can explain how binary sequences are used to represent digital data.

Introduction

This topic was covered in class on Monday.

Representing Things with Bits (Binary Strings)

A byte is an 8-bit sequence. Historially an 8-bit byte was used to represent a single character in computer memory.

The length of a binary sequence -- a sequence of 0s and 1s -- determines the number of different sequences that can be generated and therefore the number of different things that can be represented by such a sequence.

For example, with 1 bit, you can have two different sequences, 0 or 1, which can stand for two different colors, say, 0 stands for white and 1 for black. With 2 bits, you can have four different sequences, 00, 01, 10, or 11, which can represent four different colors, white, black, red, green. And so on.

In general, an n-bit sequence can represent 2ⁿ different things. Here's how:

Number of bits	Number of things	Representations
1	2 (i.e., 21)	0, 1
2	4 (i.e., 22)	00, 01, 10, 11
3	8 (i.e., 23)	000, 001, 010, 011, 100, 101, 110, 111
4	16 (i.e., 24)	0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111
5	32 (i.e., 25)
6	64 (i.e., 26)
7	128 (i.e., 27)
8	256 (i.e., 28)

Quiz Yourself

• Powers of Two

Getting Help

In Class on Friday