इंट्रस्टिंग बनने के लिए आपको इंट्रस्टेड होना पड़ेगा। If you want to become interesting then you need to be interested.

Binary Numbers

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. On Off

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 K: (kilobyte); about 1,024 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 System Humans have 10 fingers: count in DECIMAL Numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... Use 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9   We know that 5304 = 5*103+3*102+0*101+4*100 Base 10

Binary System BINARY numbers: Written with only 2 digits: "0" and "1" 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, .... Written with only 2 digits: "0" and "1" In the same way as for decimal, 1011 (binary) = 1*23+0*22+1*21+1*20= 11 (decimal) Base 2 Converting from binary to decimal is simple, just as for 1011 above.

Binary System (contd.) How to know if 1011 is in binary or in decimal? Subscripts are used to show the base: 10112 (binary number), 101110 (decimal number) Converting from decimal to binary a little bit more tricky, Let us discuss some examples.

Conversion of decimal to binary Convert 41 into a binary number Integer Quotient Remainder Coefficient 41/2=20 1/2 a0 =1 20/2=10 a1 =0 10/2=5 a2 =0 5/2=2 1/2 a3 =1 2/2=1 a4 =0 1/2 a5 =1 So (41)10 = (a5a4a3a2a1a0) = (101001)2

Conversion of decimal to binary Convert (0.6875)10 to binary Fraction Integer + fraction Coefficient 0.6875x2 1+0.3750 a-1 = 1 0.375x2 0+0.750 a-2 = 0 0.750x2 1+0.500 a-3 = 1 0.500x2 1+0.000 a-4 = 1 Hence(0.6875)10=(0.a-1a-2a-3a-4)2=(0.1011)2

Binary to decimal conversion A binary number can be converted to a decimal by forming the sum of powers of 2 of those coefficients whose value is 1. 3 2 1 -1 -2 -3 (1010.011)2= 23+21+2-2+2-3 =(10.375)10

Example Decimal            Binary      Octal           Hex   (base 10)          (base 2)    (base 8)       (base 16)       0                0000        0              0       1                0001        1              1       2                0010        2              2       3                0011        3              3       4                0100        4              4       5                0101        5              5       6                0110        6              6       7                0111        7              7       8                1000       10              8       9                1001       11              9       10               1010       12              A       11               1011       13              B       12               1100       14              C       13               1101       15              D       14               1110       16              E       15               1111       17              F 35            10 0011       43              23     100          110 0100      144              64      255        1111 1111      377              FF