The Binary System

What is the definition of binary?

Relating to, composed of, or involving two things.

How many digits does the decimal system have?

Ten digits. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

What is the base in the decimal system?

Base 10.

In the decimal system, each column (place value) is increased by?

10 X

How many digits make up the binary system?

Two (0, 1)

What is the base in the binary system?

Two.

What is a BIT?

A Binary digit.

In the binary system, each column (place value) is increased by?

2 X

What is 101 equal to in the binary system?

5 because… [(1 × 4) + (0 × 2) + (1×1) = 5]

What is the formula in the binary system used to determine the number of bits that can be represented by “n” bits?

2^n

2^1 =

2

2² =

4

2³ =

8

2^4 =

16

2^5 =

32

2^6 =

64

2^7 =

128

2^8 =

256

2^9 =

512

2^10 =

1024

What is the formula for determining the highest value that can be stored using “n” bits?

2^n - 1

What is the highest value that can be stored using 3 bits?

2³ - 1 = 7

What is bit size/depth?

The number of bits used to represent a value (ie. 10110 has 5 bits).

The binary system is… ?(3)

• Unwieldy for humans

• Great for digital machines (on vs off and also very stable)

• Large values can be stored if you have sufficient BIT depth

Current computers have a bit depth of what two options?

32 or 64

What is the primary use for the binary system?

Used in computers/technology.