Positional Number Systems Different Representations of Natural Numbers XXVII Roman numerals(not positional) 27 Radix-10 or decimal number(positional) 110112 Radix-2 or binary number (also positional) Examples:(11011)2=1×24+1×23+0×22+1×2+1=27 (2103)4=2×43+1×42+0×4+3=147 大学计算机基础教学资源库
6 Different Representations of Natural Numbers XXVII Roman numerals (not positional) 27 Radix-10 or decimal number (positional) 110112 Radix-2 or binary number (also positional) Examples: (11011)2 = 1×2 4 + 1×2 3 + 0×2 2 + 1×2 + 1 = 27 (2103)4 = 2×4 3 + 1×4 2 + 0×4 + 3 = 147 Positional Number Systems
The binary system is also called the base-2 system. (101100.011) Our decimal system is the base-10 system.It uses powers of 10 for each position in a number.(975.3) Any integer quantity can be represented exactly using any base (or radix).(3077 octal or 2BAD hex) 大学计算机基础教学资源库
7 ⚫ The binary system is also called the base-2 system. (101100.011) ⚫ Our decimal system is the base-10 system. It uses powers of 10 for each position in a number. (975.3) ⚫ Any integer quantity can be represented exactly using any base (or radix). (3077 octal or 2BAD hex)
Decimal 678.34=6×10+⑦X①+8×100+3×044×102 Radix 7 4532.1=4×73+5×72+3×71+2×70+1×71 大学计算机基础教学资源库
Decimal 678.34=6×102+7×101+8×100+3×10-1+4×10-2 Radix 7 4532.1 =4×7 3+5×7 2+3×7 1+2×7 0+1×7 -1