wyatt powers of 2

powers of 2

We use digits on a daily basis to quantify and control the things in our lives. We live in a DECIMAL world - base 10 - with digits 0-9.

For example: To make license plates that only have 3 DECIMAL (0-9) digits, we could make 1000 unique plates (000-999) which is 10^3.

With computers, we typically put digits together for a wide array of uses, but the computer uses BINARY digits (0-1).

For example, representing colors: How many colors could we represent with 3 BINARY digits? We could represent 8 colors (000-111) which is 2^3.

It is good to develop an intuitive sense of the ranges associated with n bits.

n	2^n	Range: unsigned	Range: signed (2's comp.)	Name
1 bit	2	0 .. 1		1 bit
2 bits	4	0 .. 3	-2 .. 1	2 bits
4 bits	16	0 .. 15	-8 .. 7	nibble
8 bits	256	0 .. 255	-128 .. 127	byte
16 bits	65,000+ (64k)	0 .. 65,535	-32,768 .. 32,767	word
32 bits	4 billion+	0 .. 4,294,967,295	-2,147,483,648 .. 2,147,483,647	longword
64 bits		0 .. 18,446,744,073,709,551,615	-9,223,372,036,854,775,808 .. 9,223,372,036,854,775,807	quadword

How many colors can be represented with 4 bits? 8? 16? 24? 32? Tradeoffs when representing images?

How many bytes of memory can be addressed with 4 bits? 8 ? 16? 20? 30? 32? 64? Addresses are how long in most machines? Each address is the address of a what?