2.2 General Positional-Number-System Conversion Binary, octal or hexadecimal to decimal Examples Return Next

2.2 General Positional-Number-System Conversion Decimal to binary, octal or hexadecimal When D is a integer Return Back Next

2.2 General Positional-Number-System Conversion Divide D by r the remainder will be c0. Furthermore, the quotient Q has the same form as the oriental D. Therefore, successive divisions by 2 yield successive digits ci of D from right to left, until all the digits of d have been derived. Return Back Next

2.2 General Positional-Number-System Conversion Examples 252=12 remainder 1 c0 2=6 remainder 0 c1 2=3 remainder 0 c2 2=1 remainder 1 c3 2=0 remainder 1 c4 2510=110012 Return Back Next

2.2 General Positional-Number-System Conversion Simply 8 22 (3 179 2 89 (1 179 (LSB) 8 2 (6 8 (2 2 44 (1 2 22 (0 2 11 (0 17910=2638 2 5 (1 2 (1 16 11 (3 179 1 2 (0 16 (B 2 (1 (MSB) 17910=B316 17910=101100112 Return Back Next

2.2 General Positional-Number-System Conversion When D is a fraction Multiply D by r. Return Back Next

2.2 General Positional-Number-System Conversion The integer will be c-1. Furthermore, the fraction of the product P has the same form as the oriental D. Therefore, successive multiply by r yield successive digits c-i of D from left to right, until the error is satisfying. . Examples 0.625 2=0.25+1 integer 1 c-1 2=0.5+0 integer 0 c-2 2=0.0+1 integer 1 c-3 0.62510=0.1012 Return Back Next

2.2 General Positional-Number-System Conversion Converting with six significant digits. 0.7262 0.7268 1) 0.4522 5) 0.8088 0) 0.9042 6) 0.4648 1) 0.8082 3) 0.7128 1) 0.6162 5) 0.6968 1) 0.2322 5) 0.5688 0) 0.464 4) 0.544 0.72610  0.1011102 0.72610  0.5635548 Return Back Next

2.2 General Positional-Number-System Conversion Binary to octal or hexadecimal Examples 1000110011102 = 100 011 001 1102 = 43168 1000110011102 = 1000 1100 11102 = 8CE16 10.10110012 = 010.101 100 1002 = 2.5448 10.10110012 = 0010.1011 00102= 2.B216 Octal or hexadecimal to binary Examples 5.678= 101.110 111 3.A516= 11.1010 0101 Return Back Next

2.2 General Positional-Number-System Conversion bit, byte, word, and nibble bit –– one binary digit is called bit. byte –– 8 binary digits is called byte. word –– n-bit word means one word has n binary digits. nibble –– 4-bit or half-byte is called nibble. Example A hexadecimal number is 5678ABCD16 . How many binary digits has it? How many 8-bit bytes has it? What is the hexadecimal value of every 8-bit byte? How many 2-byte words has it? How many 32-bit words has it? Return Back Next

2.2 General Positional-Number-System Conversion Answer 5678ABCD16 =0101 0110 0111 1000 1010 1011 1100 11012 It has 32 binary digits. It has four 8-bit bytes. The hexadecimal values of four 8-bit bytes are 5616, 7816, AB16, CD16. It has two 2-byte words. It has one 32-bit word. A file’s size is 20bytes. How many 1-bit memory units need for saving this file? If a file’s size is 1kbytes? Return Back