===============Number Systems|===============1) Decimal Number System========================10 Symbols0,1,2,3,4,5,6,7,8,9(Base 10)------------------------Place Value7543--------------------------------------| Thousands | Hundreds | Tens | Ones |--------------------------------------| 10^3 | 10^2 | 10^1 | 10 |--------------------------------------| 7 | 5 | 4 | 3 |--------------------------------------Expanded Notation: 7x10^3 + 5x10^2 + 4x10^1 + 3x10^0 7x1000 + 5x100 + 4x10 + 3x1 (*) Binary===========2 Symbols : 0,1()Base 2)-----------Place Value101-------------------------------------| 2^5 | 2^4 | 2^3 | 2^2 | 2^1 | 2^0 |------------------------------------- | 1 | 0 | 1 |-------------------------------------Expanded Notation: 1x2^2 + 0x2^1 + 1x2^0 4 + 0 + 1 = 5 (ie, 101 in binary = 5 irl)(*) Hexadecimal===============16 Symbols: 0-9 and A-F (aka 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F)(Base 16)---------------Place Value101----------------------| 16^2 | 16^1 | 16^0 |----------------------| 1 | 0 | 1 |----------------------Exoanded Notation: 1x16^2 + 0x16^2 + 1x16^0 1x256 + 0 + 1 = 256+1 = 257(*) Notation of Number Systems==============================Binary System 101(Subscript 2) 101(Subscript b)Decimal System 101(Subscript 10) 101(Subscript d)Hexadecimal System 101(Subscript 16) 101(Subscript h)(*) Conversion between Bases============================1) Remainder Method-------------------*Decimal -> Any base-> Convert 76(Subscript 10) to Binary(Base 2)2|76|02|38|02|19|02| 9|1 (Read it from Down to Up) => 1001100(Subscript/Base 2)2| 4|12| 2|02| 1|0 ---- | 0| 2) Place Value Method---------------------> Decimal to Binary for 76(base 10)-------------------------------------|2^8|2^7|2^6|2^5|2^4|2^3|2^2|2^1|2^0|-------------------------------------|256|128| 64| 32| 16| 8| 4| 2| 1|-------------------------------------=> 76(Base 10) 64 ---- 12 8 ---- 44 ---- 0=> 1001100-> Convert 76(Base 10) to Hexadecimal(Base 16) |Remainder16|76|1216| 4| 4 ---- 0 => 76(Base 10) = 4C(Base h) ----=> Conversion between Binary to Hexadecimal-------------------------------------------Binary => Base 2=> 2^4 => Group the symbols in 4's from right to left. Then determine the decimal/hex equivalent of each group of 4.Hexadecimal => Base 16=> Ex-> 11011011011(Base 2) to Base 16* Group symbols in 4's=> 110|1101|1011Add zero to left if its not in group of 4=> 0110|1101|1011Convert each group individually-----------------|2^3|2^2|2^1|2^0| (0110|1101|1011)----------------- ----| 1 | 0 | 1 | 1 |-----------------=> 1x8 + 0x4 + 1x2 + 1x1 = 8+2+1 = 11Do same for other two.=> Conversion between Hexadecimal to Binary-------------------------------------------Hex=>Binary-> For each Hexadecimal symbol identify the binary equivalent using group of 4 symbols=> Ex-> 751(Base h) => 0111 0101 0001 (Make sure its group of 4's or add 0's to left) - - --- -> 157(Base h) => 0001 0101 0111 ==========================Exercise==========================3) Count from 10101b to 11010b, writing all binary numbers in between.A-> 10101, 10110, 10111, 11000, 11001, 11010(Method:)10110+ 1----- (Carry 1) (Carry 1) (Carry 1) 1 0 1 1 1+ 1-------------------------------------1 1 0 0 0-------------------------------------03E8 = 40 hours0x16^3 + 3x16^2 + 14x16^1 + 8x16^0 = 0+768+224+8 = 1000 => 40 hours1000/40 = 2516 25 916 1 1 0 => 19 = hourly rate A1E7102 10 02 5 12 2 0 1 11010 0001 1101 2 14 02 7 12 3 12 1 11001000011111011