3. (10 marks) As mentioned in this week's notes, writing values in binary can get quite tedious: They take a lot of typing - typically three to four times as many digits as the equivalent decimal representations - and transposing long strings of Is and Os is an error-prone activity. On the other hand, translating from binary (also called "base two") into decimal (base ten") and vice-versa is a tedious business. Consequently, computer scientists and computer engineers long ago started representing values in number bases that were powers of two, which makes translation to and from binary casier, For a long time, octal ("base cight") was popular, and it is still used for some things, but a more common representation is hexadecimal, which is base sixteen, often abbreviated to her. Hex requires 16 symbols for its numerals. It borrows the first 10 symbols from decimal and the last six from the beginning of the alphabet, so that each hex digit represents a pattern of four bits as follows: binaryd hexsi decimal binary hex decimale 0000 0 0 1000 8 0001 12 1001 9 9 0010 2 2 1010 A 10 3e 3e 1011er 0100 1100- C 12 0101 5 54 1101 D 13 le 0110 1110 14 0111 7 1111 F 150 8 9 0011 Be Ee 66 73 Thus, hex is more economical than decimal since some 2-digit decimal values can be written in 1 hex digit (1 Osecimal Alex, 11 decimal = Bho, 12 decimal = Chex, 13.decimal Dec. 14decimal Ew, and 15 decimal = Ewe). Website builders are familiar with hex because it is the notation most frequently used to specify colour values for web pages. The column values in a hex number are powers of 16, 80, for example, 2345x 2 x 16 + 3 * 16 + 4 x 16' +5 x 16 -9029 decimal What are the decimal and binary equivalents of the following hex numbers? (Great Big Hint: Just copy the bit patterns from the chart above for the hex-to-binary conversions. Use 8 bits for your binary solutions to the first three problems, and 16 bits for the last two. I have solved the first one for you and highlighted where the bit patterns were copied from. You do not have to do any highlighting. Decimale 23e W e Hexe Binary (8-bit) 17e 0001 0111e a) 1 0001 1111 b) 20e 0010 0000 c) FFA 1111 1111e d) 100- e) CBAgele le 20121212 e 4. (2 mark) In the table below, type the last two digits of your student number in decimal, then in 8-bit binary, then in hexadecimal Hex Decimal Binary 300