A Bit About Bits

A bit (binary digit)

– is the smallest unit of information

– can have two values 1 and 0.

Binary digits, or bits, can represent numbers, codes, or instructions.

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Bits as Numbers

Binary number system -a system that denotes all numbers and combinations of two digits.

The binary system uses two digits to represent the numbers, 0 and 1.

Bits, Bytes, and Buzzwords

Common terms might describe file size or memory size:

Bit: smallest unit of information

Byte: a grouping of eight bits of information

KB: (kilobyte); about 1,000 bytes of information - technically 1024 bytes equals 1K of storage.

Bits, Bytes, and Buzzwords

MB: (megabyte); about 1 million bytes of information

GB: (gigabyte); about 1 billion bytes of information

TB: (terabyte); about 1 million megabytes of information

Decimal number system

• Ten digits : 0,1,2,3,4,5,6,7,8,9

• Every digit position has a weight which is a power of 10.

• Base or radix is 10.

Binary number system

Two digits : 0,1

Every digit position has a weight which is a power of 2.

Base or radix is 2.

Decimal Number

• 136.25 : What does this number actually mean ?

102 * 1 = 100.0

101 * 3 = 30.0

100 * 6 = 6.0

10-1 * 2 = 0.2

10-2 * 5 = 0.05

Binary Number

• 1101.01: What does this number mean?

23 * 1 = 1000.0 (8 in decimal)

22 * 1 = 100.0 (4 in decimal)

21 * 0 = 00.0 (0 in decimal)

20 * 1 = 1.0 (1 in decimal)

2-1 * 0 = 0.0 (0.0 in decimal)

2-2 * 1 = 0.01 (0.25 in decimal)

First integers and their binary equivalent

decimal binary

0 0000 (0*23 + 0*22 + 0*21 + 0*20)

1 0001 (0*23 + 0*22 + 0*21 + 1*20)

2 0010 (0*23 + 0*22 + 1*21 + 0*20)

3 0011 (0*23 + 0*22 + 1*21 + 1*20)

4 0100 (0*23 + 1*22 + 0*21 + 0*20)

5 0101 (0*23 + 1*22 + 0*21 + 1*20)

6 0110 (0*23 + 1*22 + 1*21 + 0*20)

7 0111 (0*23 + 1*22 + 1*21 + 1*20)

8 1000 (1*23 + 0*22 + 0*21 + 0*20)

9 1001 (1*23 + 0*22 + 0*21 + 1*20)

Decimal (base 10)

• Uses positional representation

• Each digit corresponds to a power of 10 based on its position in the number

• The powers of 10 increment from 0, 1, 2, etc. as you move right to left

1,479 = 1 * 103 + 4 * 102 + 7 * 101 + 9 * 100

Binary (base 2)

• Two digits: 0, 1

• To make the binary numbers more readable, the digits are often put in groups of 41010 = 1 * 23 + 0 * 22 + 1 * 21 + 0 * 20

= 8 + 2 = 10

1100 1001

= 1 * 27 + 1 * 26 + 1 * 23 + 1 * 20

= 128 + 64 + 8 + 1 = 201