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1.29" 1.32* 133° 36 Chapter 1 1.34 1.35 should algebra, the space. Treat the leftmost bit of each character as a parity bit. Each eight-bit cod have odd parity. (George Boole was a 19th-century mathematician, Bool introduced in the next chapter, bears his name.) Decode the following ASCII code LOLOOTL 1110100 1100101 1110110 1100101 0100000 1001010 1101111 1100010 1110011. The following is a string of ASCII characters whose bit patterns have been converted into actness: 73 F4 ES 76 ES 4A EF 62 73, Of the eight bits in each pair of digits, the leftmost is a parity bit. The remaining bits are the ASCII code (a) Convert the str ing to bit form and ode the ASCIL (b) Determine the parity used: odd or even? hexadecimal for com How many printing characters are there in ASCII? How many of them are special char- acters (not letters or numerals)? What bit must be complemented to change an ASCII letter from capital to lowercas vice versa? and ‘The state of a 12-bit register is 100010010111. What is its content if it represents (a) Three decimal digits in BCD? (b) Three decimal digits in the excess-3 code? (c) Three decimal digits in the 84-2-1 code? (d) A binary number? igital Systems and Binary Numbers List the ASCH code for the 10 decimal digits with an even parity bit in the leftmost position Bym s of a timing diagram similar to Fig, 1.5, show the signals of the outputs f and g in Fig. P1.35 as functions of the three inputs a, b, and ¢. Use all eight possible combinations of a,b, and c u FIGURE P1.35 By means of a timing diagram similar to Fig. 1.5,show the signals of the outputs f and g in P1.36 as functions of the two inputs a and b, Use all four possible combinations of a and b, FIGURE P1.36 REFERENCES Cavanacn, J. J. 1984. Digital Computer Arithmetic. New York: McGraw-Hill. , M. M, 1988. Computer Engineering: Hardware Design. Englewood Cliffs, NJ: *ROBLEM its output becomes logic 0 only when all inputs are logic 0. Ss (Answers to problems marked with * appear at the end of the text.) 1.2° 1.4 1.5" 1.6" List the octal and hexadecimal numbers from 16 to 32. Using A and B for the last two digits, list the numbers from 8 to 28 in base 12 What is the exact number of bytes in a system that contains (a) 32K bytes, (b) 64M bytes, and (c) 6.4G bytes? Convert the following numbers with the indicated bases to decimal (a)* (4310); (by" (198))> {c) (435) (d) (345), What is the largest binary number that can be expressed with 16 bits? What are the equiv- alent decimal and hexadecimal numbers? Determine the base of the numbers in each case for the following operations to be correct: (a) 142=5 (b) 54/4=13 (c) 24417 =40. The solutions to the quadratic equation a? — Lx + 22 =0 are x = 3 and x = 6. What is the base of the numbers? ‘4 Chapter 1 Digital Systems and Binary Numbers 1.7" 1.8 1.9 1.11 1,12* Convert the hexadecimal number 64CD to binary, and then convert it from binary to octal. ) convert directly to binar inary. Which method is faster? imal number 431 to bi in two way (b) convert first to hexadecimal and then from hexadecimal to Express the following numbers in decimal. (ay* (10110.0101); (by" (16.5)t5 (c)" (26.24)y (d) (DADA.B) 5 (e) (10101101), Convert the following binary numbers to hexadecimal and to decimal: (a) 1.10010, (b) 110.010. Explain why the decimal answer in (b) is 4 times that in (a). Perform the following division in binary: 111011 + 101 Add and multiply the following numbers without converting them to decimal, (a) Binary numbers 1011 and 101 (b) Hexadecimal numbers 2E and 34. Do the following conversion problems: (a) Convert decimal 27315 to binary. (b) Calculate the binary equivalent of 3 out to cight places. Then convert from binary to decimal, How close is the result to 2 ry result in (b) into hexadecimal. Then convert the result to decimal. Is the answer the san Obtain the 1's and 2's complements of the following binary numbers: (a) 00010000 (b) 00000000 (c) 11011010 (d) 10101010 (e) LO000101 (f) Tn. Find the 9's and the 10's complement of the following decimal numbers: (a) 25,478,036 (b) 63, 325,600 {c) 300,000 (d) 00,000,000. (a) Find the 16's complement of C3DF. (b) Convert C3DF to binary. (c) Find the 2's complement of the result in (b). (d) Convert the answer in (c) to hexadecimal and compare with the answer in (a). Perform subtraction on the given unsigned numbers usi ubtrahend. Where the result should be negative, find its 10’ gn. Verify your answers. (a) 4,637 579 (b) 125 — 1,800 (c) 2,043 - 4,361 (d) 1,631 — 745 Perform subtraction an th g the 10's complement of the ‘complement and affix a minus given uinsioned binary numbers usine the 2’s eamnlement af the Few points to be considered for Assignment 1: 1- For Q 1: You will have to use ASCII equivalent for all characters from ASCII table. For example: ASCII equivalent for A = (41)... = (65)i9 = (101)g,. 2- Union of string will have unique elements being used in all the strings. For the given example in assignment, union will be like ={1m, u, fh, a, 4, y,5,i, 1, 7} 3- Assuming some values of x3 = 3,x%4 = 6 then (%g%9.%4)g = (33.6)g. There is no multiplication operator in the expression. | g. Find £’s complement of (%6%2%4X4Xs) 16: 7 im. ua. 3)6 7 - (OFD}Ié ne ~_( 326 jie _ Questions Related £0 Complement wel 1:2 ; 165 complemen 7 felose. oon 7 46 = wio0-FE— 106 — = — — . Too FO} OYVP ier! = | ci, aie () we ae ul . a = POEE Vie. }-~ ne 0 ji S* LOWE = é 7 ¥ ———————— aoe © © M.| (Question. tof Complement = ; Not AND OR 1 - (+87). Ba)4AC a Uiskc}, Ba) Draw Civewit + Se eae aan? f F u i D D im) [ss 28a af ~~ a A ¥ ro w wii in fe i al a 4 } = _—__— | NON implementers < 
