Introduction Number Systems and Conversion

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24 Unit 11.3 Convert to base 6: 3BA.25 14 (do all of the arithmetic in decimal).1.4 (a) Convert to hexadecimal: 1457.11 10 . Round to two digits past the hexadecimal point.(b) Convert your answer to binary, and then to octal.(c) Devise a scheme for converting hexadecimal directly to base 4 and convert youranswer to base 4.(d) Convert to decimal: DEC.A 16 .1.5 Add, subtract, and multiply in binary:(a) 1111 and 1010 (b) 110110 and 11101 (c) 100100 and 101101.6 Subtract in binary. Place a 1 over each column from which it was necessary to borrow.(a) 11110100 1000111 (b) 1110110 111101 (c) 10110010 1111011.7 Add the following numbers in binary using 2’s complement to represent negative numbers.Use a word length of 6 bits (including sign) and indicate if an overflow occurs.(a) 21 11 (b) (14) (32) (c) (25) 18(d) (12) 13 (e) (11) (21)Repeat (a), (c), (d), and (e) using 1’s complement to represent negative numbers.1.8 A computer has a word length of 8 bits (including sign). If 2’s complement is used torepresent negative numbers, what range of integers can be stored in the computer?If 1’s complement is used? (Express your answers in decimal.)1.9 Construct a table for 7-3-2-1 weighted code and write 3659 using this code.1.10 Convert to hexadecimal and then to binary.(a) 1305.375 10 (b) 111.33 10 (c) 301.12 10 (d) 1644.875 101.11 Convert to octal. Convert to hexadecimal. Then convert both of your answers todecimal, and verify that they are the same.(a) 101111010100.101 2 (b) 100001101111.01 21.12 (a) Convert to base 3: 375.54 8 (do all of the arithmetic in decimal).(b) Convert to base 4: 384.74 10 .(c) Convert to base 9: A52.A4 11 (do all of the arithmetic in decimal).1.13 Convert to hexadecimal and then to binary: 544.1 9 .1.14 Convert the decimal number 97.7 10 into a number with exactly the same value representedin the following bases. The exact value requires an infinite repeating partin the fractional part of the number. Show the steps of your derivation.(a) binary (b) octal (c) hexadecimal (d) base 3 (e) base 51.15 Devise a scheme for converting base 3 numbers directly to base 9. Use your methodto convert the following number to base 9: 1110212.20211 3
Number Systems and Conversion 251.16 Convert the following decimal numbers to octal and then to binary:(a) 2983 63 / 64 (b) 93.70 (c) 1900 31 / 32 (d) 109.301.17 Add, subtract, and multiply in binary:(a) 1111 and 1001 (b) 1101001 and 110110 (c) 110010 and 111011.18 Subtract in binary. Place a 1 over each column from which it was necessary to borrow.(a) 10100100 01110011 (b) 10010011 01011001(c) 11110011 100111101.19 Divide in binary:(a) 11101001 101 (b) 110000001 1110 (c) 1110010 1001Check your answers by multiplying out in binary and adding the remainder.1.20 Divide in binary:(a) 10001101 110 (b) 110000011 1011 (c) 1110100 10101.21 Assume three digits are used to represent positive integers and also assume the followingoperations are correct. Determine the base of the numbers. Did any of theadditions overflow?(a) 654 013 000(b) 024 043 013 033 223(c) 024 043 013 033 2011.22 What is the lowest number of bits (digits) required in the binary number approximatelyequal to the decimal number 0.6117 10 so that the binary number has thesame or better precision?1.23 Convert 0.363636. . . 10 to its exact equivalent base 8 number.1.24 (a) Verify that a number in base b can be converted to base b 3 by partitioning thedigits of the base b number into groups of three consecutive digits starting at theradix point and proceeding both left and right and converting each group intoa base b 3 digit. (Hint: Represent the base b number using the power seriesexpansion.)(b) Verify that a number in base b 3 can be converted to base b by expanding eachdigit of the base b 3 number into three consecutive digits starting at the radixpoint and proceeding both left and right.1.25 Construct a table for 4-3-2-1 weighted code and write 9154 using this code.1.26 Is it possible to construct a 5-3-1-1 weighted code? A 6-4-1-1 weighted code? Justifyyour answers.1.27 Is it possible to construct a 5-4-1-1 weighted code? A 6-3-2-1 weighte code? Justifyyour answers.
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