Please check if I did the following correctly. Thanks. Basically, #1 and #4 I need help with (those are primary) and #2,#3 i need you to check if i did it correctly.

Reduce the following SE's to number of literals specified.

bc'd(a+1) + ab'(c+c') + cd(a+a'b)

bc'd + ab' + cd(a+b)

bc'd + ab' + acd + bcd

bd(c+c') + ab' + acd

bd + ab' + acd (From here, I have 7 literals, and I don't know what to do. I've tried the following but i still end up with 6 literals and can't get 4)

ab'(d+d') + bd(a+a') + acd

ab'd + ab'd' + abd + a'bd + acd

ad(b'+b) + ab'd' + a'bd + acd

ad + ab'd' + a'bd + acd

ad(1+c) + ab'd' + a'bd

ad + ab'd' + a'bd

a(d+d'b) + a'bd

a(d+b) + a'bd

ad + ab + a'bd

ad + b(a+a'd)

ad + ab + bd ... Stuck here.. What can i do? I've played with it for like 2 hours straight and can't figure it out. Any help would be greatly appreciated.

Problem 2 (I finished this, please check if its correct)

bc'(d'+d) + b'c'(ad' + a') + abc + ac'd

bc' + b'c'(a'+d') + abc + ac'd

bc' + a'b'c' + b'c'd' + abc + ac'd

b(c' + ca) + a'b'c' + b'c'd' + ac'd

b(c' + a) + a'b'c' + b'c'd' + ac'd

bc' + ab + a'b'c' + b'c'd' + ac'd

c'(b+b'a') + ab + b'c'd' + ac'd

c'(b+a') + ab + b'c'd' + ac'd

bc' + a'c' + ab + b'c'd' + ac'd

c'(b + b'd') + a'c' + ab + ac'd

c'(b + d') + a'c' + ab + ac'd

bc' + c'd' + a'c' + ab + ac'd

bc' + c'd' + c'(a'+ad) + ab

bc' + c'd' + c'(a'+d) + ab

a'c' + c'd + c'd' + bc' + ab

a'c' + c'(d+d') + bc' + ab

a'c' + c' + bc' + ab

a'c' + c'(b+1) + ab

a'c' + c' + ab

c'(a'+1) + ab

ab + c'

{[(a+b+a'c')c+d]' + ab'}

too much to type, but basically i got m(0,1,2,3,4,5,8,9,11,12) let me know if you agree with this if it disagrees ill type out what i have.

xyz + yw + x'z' + xy'

So basically to do this we just keep expanding until we get a product of maxterms? like this..:

x(yz + y') + yw + x'z'

x(y' + z) + yw + x'z'

xy' + xz + yw + x'z'

(xy' + x)(xy' + z) + (yw+x')(yw+z')

x(xy'+z) + (yw+x')(yw+z')

(xy' +xz) + (yw+x')(yw+z')

((xy'+xz)) + (yw+x'))((xy'+xz) + (yw+z'))

I dont get what i do.. if i keep expanding it gets really complicated.. any suggestions??

Reduce the following SE's to number of literals specified.

**1) abc'd + ab'c + bc'd + ab'c' + acd + a'bcd (4 Literals)**bc'd(a+1) + ab'(c+c') + cd(a+a'b)

bc'd + ab' + cd(a+b)

bc'd + ab' + acd + bcd

bd(c+c') + ab' + acd

bd + ab' + acd (From here, I have 7 literals, and I don't know what to do. I've tried the following but i still end up with 6 literals and can't get 4)

ab'(d+d') + bd(a+a') + acd

ab'd + ab'd' + abd + a'bd + acd

ad(b'+b) + ab'd' + a'bd + acd

ad + ab'd' + a'bd + acd

ad(1+c) + ab'd' + a'bd

ad + ab'd' + a'bd

a(d+d'b) + a'bd

a(d+b) + a'bd

ad + ab + a'bd

ad + b(a+a'd)

ad + ab + bd ... Stuck here.. What can i do? I've played with it for like 2 hours straight and can't figure it out. Any help would be greatly appreciated.

Problem 2 (I finished this, please check if its correct)

**2) acb + ac'd + bc'd' + a'b'c' + ab'c'd' + bc'd (3 Literals)**bc'(d'+d) + b'c'(ad' + a') + abc + ac'd

bc' + b'c'(a'+d') + abc + ac'd

bc' + a'b'c' + b'c'd' + abc + ac'd

b(c' + ca) + a'b'c' + b'c'd' + ac'd

b(c' + a) + a'b'c' + b'c'd' + ac'd

bc' + ab + a'b'c' + b'c'd' + ac'd

c'(b+b'a') + ab + b'c'd' + ac'd

c'(b+a') + ab + b'c'd' + ac'd

bc' + a'c' + ab + b'c'd' + ac'd

c'(b + b'd') + a'c' + ab + ac'd

c'(b + d') + a'c' + ab + ac'd

bc' + c'd' + a'c' + ab + ac'd

bc' + c'd' + c'(a'+ad) + ab

bc' + c'd' + c'(a'+d) + ab

a'c' + c'd + c'd' + bc' + ab

a'c' + c'(d+d') + bc' + ab

a'c' + c' + bc' + ab

a'c' + c'(b+1) + ab

a'c' + c' + ab

c'(a'+1) + ab

ab + c'

**Problem 3: Convert following SEs into sum of minterms**{[(a+b+a'c')c+d]' + ab'}

too much to type, but basically i got m(0,1,2,3,4,5,8,9,11,12) let me know if you agree with this if it disagrees ill type out what i have.

**Problem 4: Convert following SEs into product of maxterms without obtaining sum of minterms first**xyz + yw + x'z' + xy'

So basically to do this we just keep expanding until we get a product of maxterms? like this..:

x(yz + y') + yw + x'z'

x(y' + z) + yw + x'z'

xy' + xz + yw + x'z'

(xy' + x)(xy' + z) + (yw+x')(yw+z')

x(xy'+z) + (yw+x')(yw+z')

(xy' +xz) + (yw+x')(yw+z')

((xy'+xz)) + (yw+x'))((xy'+xz) + (yw+z'))

I dont get what i do.. if i keep expanding it gets really complicated.. any suggestions??

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