CS101 Solution 1

Marks(12) AliceandBobareplayingagamebyencodingtheirmessagesinan8-bitbinary. Trudy wantstounderstandormodifytheirmessages. YouhavetohelpTrudytoconvert encodedmessagesintoareadableformatbyperformingthefollowingoperations.

01001000 01101001 00101100 Encoded

BO Alice

Trud

•  Note:Performalltherequiredstepsindetailforeachoperation.

(a)Converttheabove8-digitbinarynumbersintodecimals. Solution: 010010002= (0×27)+(1×26)+(0×25)+(0×24)+(1×23)+(0×22)+(0×21)+(0×20) =0+64+0+0+8+0+0+0 010010002=7210

011010012= (0×27)+(1×26)+(1×25)+(0×24)+(1×23)+(0×22)+(0×21)+(1×20) =0+64+32+0+8+0+0+1 011010012=10510

001011002= (0×27)+(0×26)+(1×25)+(0×24)+(1×23)+(1×22)+(0×21)+(0×20) =0+0+32+0+8+4+0 001011002=4410

(B)Convertthe8-digitbinaryintohexadecimal. (3marks) Solution: ConvertbinaryvaluetoHexaDecimalValue

8421 0100 1000

010010002=4816

ConvertbinaryvaluetoHexaDecimalValue

8421 0110 1001

011010012=6916

ConvertbinaryvaluetoHexaDecimalValue 8421 0010 1100 C 001011002=2C16

(C)Decodethe8-digitbinaryintextualform.(Hint:usingtheASCIItable). (3 marks) 01001000 01101001 00101100 ACSIICodes H I TextualFormis:Hi,

Marks(04) Thediagrambelowshowsacircuitwithfourgatesandfourinputs(A,B,CandD).

Ifthefinaloutputis0,whatarethepossiblestatesofinputsA,B,CandD?

A B C D