명지대학교교과목명디지털논리회로소속정보통신공학과점수강좌번호0767학년학번담당교수동용배성명2011학년도 제 1 학기 중간고사unsignedsigned3 - 5overflowFEH127 + 127FEHoverflow--------------------------------------------------------------------1. 다음 8-bit 10진수에 대해서 연산을 할 경우, unsigned 및 signed 방식에 대한 답을 16 진수로 표기하라.11112. 다음 합의식을 Boolean 대수를 사용하여 증명하라.ab + a'c = ab + a'c + bc= ab(1+c) + a'c(1+b) = ab +abc + a'c+a'bc= ab + a'c + bc3. 합의 이론을 사용하여 다음 식을 증명하라.(x + z)(x' + y) = xy + x'z= xy + x'z + yz= xy + x'z ( 합의에 의해서)4. 1bit 전가산기 진리표를 작성하고, K-map을 이용하여 s 및 c에 대한 식을 최소화하고, 최소(9개) NAND 개수를 사용하여 설계하라.abcsc0**************************1011100111111s= abc1111c=ab + c(ab)logic circuit?5. K-map을 사용하여 다음 식을 최소화하라.f(a,b,c,d)=Σm(1,3,4,6,11) +Σd(0,8,10,12,13)11111abcdf= a'b'd + a'bd' + (ab'c or b'cd)6. K-map을 사용하여 다음 식을 최소화하라.f(a,b,c,d,e)=Σm(1,3,8,9,11,12,14,17,19,20,22,24,25,27),a=0, bc1111111dea=1, bc1111111def= c'e + bc'd' + a'bce' +ab'ce'
명지대학교교과목명디지털논리회로소속정보통신공학과점수강좌번호0749/0750학년학번담당교수동용배성명2010학년도 제 1 학기 중간고사--------------------------------------------------------------------1. For each of the following pairs of numbers, subtract the second from the first. Show the operands and the answers in decimal, assumingunsignedsigneda. 010101 001100b. 010001 011000c. 111010 000111d. 100100 011000e. 110010 110111f. *************. We have a computer which stores binary signed numbers in two's complement form. All numbers are 8 bits long.a. What decimal number is represented by 01101011 ?b. What decimal number is represented by 10101110 ?c. How is the number -113 stored ?d. How is the number +143 stored ?e. How is the number +43 stored ?f. How is the number -43 stored ?3. Prove the following equation by using consensus theory.ab + a'c = (a +c)(a' + b)4. Prove the following equation by using algebra.ac + a'd + cd = ac + a'dabcsc5. Make the truth table of a full adder, minimize the equations by using K-map, and implement the logic circuit using only two Exclusive-ORs and 3 two-input NANDs.truth tables:c:s=c=logic circuit6. Minimize the following equation by using K-map, also and the tabulation method using the Petrick's method. f(w,x,y,z)=Σm(1,3,4,5,7,9,11,12,14,15).7. Minimize costlessly the following multi-output equations by using K-map and the tabulation method, and calculate the terms and the literals (cost=45). f(a,b,c)=Σm(1,3,4,6,7), g(a,b,c)=Σm(1,2,3,6,7), h(a,b,c)=Σm(0,1,4,6,7).
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