EEE 120 Digital Design
Fundamentals: Final Exam
Prep - ASU 2025 Spring
Session A QUESTIONS AND
VERIFED CORRECT
ANSWERS GRADED A+
[LATEST] 100% GUARANTEED
PASS
How to implement an arbitrary Boolean function using AND/OR/NOT gates, using only NAND
gates, and using only NOR gates - CORRECT ANSWER-Types of gates you can recreate using
NAND:
NOT - One NAND gate
AND - One NAND gate in front of the other
OR - Two NAND gates side by side feeding into one NAND
Types of gates you can recreate using NOR:
NOT - One NOR gate
OR - One NOR gate in front of the other
AND - Two NOR gates side by side feeding into one NOR
Note* You can cancel out two NOTs/NANDs/NORs
,How to represent a number in different bases (Base- 2, base- 8, base- 10, base- 16) - CORRECT
ANSWER-Binary Base-2: 00, 01, 10, 11, 100, 101, 110, 111
Octal Base-8: 0, 1, 2, 3, 4, 5, 6, 7, 10
Decimal Base-10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Hexadecimal Base-16: 1, 2, 3, 4, 5, 6, 7, 8, 9, A,B,C,D,E,F
How can you convert between base 2 and the others? - CORRECT ANSWER-Base2->Base8 =
Break binary into groups of 3 with 4, 2, 1 beneath each group. If, say, you have a 1 above 4, add
4 to the number. If you have a 0 above your 2, don't add the 2.
Base2->Base10 = Beneath the binary, use your 2^#column number starting with 0. If it's 1 in, say
the 0 column, use that 2^0 and add 1 to your number, and so on.
Base2->Base16 = Group into 4's and label beneath them 8, 4, 2, 1 accordingly. If it's under a 1,
add it to your number. 10 and up? Use letters
How can you convert between base 8 and the others? - CORRECT ANSWER-Base8->Base2 =
Break number into pieces, put 4 2 1 beneath each number and circle what makes up the
number piece. If your number piece was 5, circle 4 and 1 which makes up 101
Base8->Base10 = Each number is made up of 8^#column number starting with 0. Multiply the
8^# by the number in that column. Say it's 37...7 is underneath 8^0 so multiply 8^0 by 7
Base8->Base16 = Split the number into individual numbers with 421 beneath them. Let's say
your number is 213. You would circle 2 for 2, 1 for 1, and 2 & 1 to make up 3....next you would
place a 1 underneath the numbers you circled then put those numbers into groups of 4. That
comes out to 1000, which is 8, and 1011, which is 11 or B. The answer comes out to 8B.
How can you convert between base 10 and the others? - CORRECT ANSWER-Base10->Base2 =
Start with listing the powers of 2 from the greatest you know to least. For example: 128, 64, 32,
16, 8, 4, 2, 1. Pick the number that can fit into your number the best. So, say if your number is
75, 64 fits in the best. Then take the lesser numbers from greatest to least that fit into the
number until you have added up to your number. 8, 2, and 1 with 64 would add up to 75. Put 1's
below the numbers you needed to add up to your number and 0's over the ones that were not
used. You should end up with 1001011
, Base10->Base8 = Divide by 8 and collect the remainders starting with the last remainder to the
first, and that is your new number
Base10->Base16 = Divide by 16 and collect the remainders starting with the last remainder to
the first, and that is your new number
How can you convert between base 16 and the others? - CORRECT ANSWER-Base16->Base2 =
Take your number piece by piece. So if you had A9, you would take your A, translate it to
decimal (10), and underneath it write 8421. Circle the values that add up to 10 (8 and 2) and put
1's underneath each one you circle and 0's for the numbers you don't. You should end up with
1010. Do the same with 9. You will end up circling 8 and 1, which comes out to 1001. Put them
together, left to right, and you get your binary conversion 10101001.
Base16->Base8 = Take your number, say AC, and break it into chunks. A is 10, and C is 12. Put
8421 underneath both and circle the values that add up to A and C. If you put a 1 under the
values you circled and a 0 under the values you did not circle, you will get 0's and 1's that you
need to group into 3's. Put 421 underneath your 0's and 1's and circle the values your 1's align
with. So you should have 010 101 100, which translates to 254
Base16->Base10 = Say you have 23E. Breaking it into pieces, you will have to use 16^to the
power of each column's value starting at 0, and you multiply that by your number chunk. In our
case, we would start with E, which is 14 in decimal. So that would be 16^0 * 14, and we would
add it to every other value. 16^0 * 14 + 16^1 * 3 + 16^2 * 2, which comes out to our decimal
conversion 574.
2's complement representation of signed binary numbers - CORRECT ANSWER-the most
significant bit (leftmost digit) acts as the sign bit, where a '0' indicates a positive number and a
'1' indicates a negative number
2's complement operation - CORRECT ANSWER-To represent a negative number, you take the
binary representation of its positive counterpart, flip all the bits (one's complement), and then
add 1 to get the 2's complement representation
Identify the overflow conditions. How does it work? - CORRECT ANSWER-Add the numbers
together. The carry MostSignificantBit is the last value you carry over before the carry out,
Fundamentals: Final Exam
Prep - ASU 2025 Spring
Session A QUESTIONS AND
VERIFED CORRECT
ANSWERS GRADED A+
[LATEST] 100% GUARANTEED
PASS
How to implement an arbitrary Boolean function using AND/OR/NOT gates, using only NAND
gates, and using only NOR gates - CORRECT ANSWER-Types of gates you can recreate using
NAND:
NOT - One NAND gate
AND - One NAND gate in front of the other
OR - Two NAND gates side by side feeding into one NAND
Types of gates you can recreate using NOR:
NOT - One NOR gate
OR - One NOR gate in front of the other
AND - Two NOR gates side by side feeding into one NOR
Note* You can cancel out two NOTs/NANDs/NORs
,How to represent a number in different bases (Base- 2, base- 8, base- 10, base- 16) - CORRECT
ANSWER-Binary Base-2: 00, 01, 10, 11, 100, 101, 110, 111
Octal Base-8: 0, 1, 2, 3, 4, 5, 6, 7, 10
Decimal Base-10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Hexadecimal Base-16: 1, 2, 3, 4, 5, 6, 7, 8, 9, A,B,C,D,E,F
How can you convert between base 2 and the others? - CORRECT ANSWER-Base2->Base8 =
Break binary into groups of 3 with 4, 2, 1 beneath each group. If, say, you have a 1 above 4, add
4 to the number. If you have a 0 above your 2, don't add the 2.
Base2->Base10 = Beneath the binary, use your 2^#column number starting with 0. If it's 1 in, say
the 0 column, use that 2^0 and add 1 to your number, and so on.
Base2->Base16 = Group into 4's and label beneath them 8, 4, 2, 1 accordingly. If it's under a 1,
add it to your number. 10 and up? Use letters
How can you convert between base 8 and the others? - CORRECT ANSWER-Base8->Base2 =
Break number into pieces, put 4 2 1 beneath each number and circle what makes up the
number piece. If your number piece was 5, circle 4 and 1 which makes up 101
Base8->Base10 = Each number is made up of 8^#column number starting with 0. Multiply the
8^# by the number in that column. Say it's 37...7 is underneath 8^0 so multiply 8^0 by 7
Base8->Base16 = Split the number into individual numbers with 421 beneath them. Let's say
your number is 213. You would circle 2 for 2, 1 for 1, and 2 & 1 to make up 3....next you would
place a 1 underneath the numbers you circled then put those numbers into groups of 4. That
comes out to 1000, which is 8, and 1011, which is 11 or B. The answer comes out to 8B.
How can you convert between base 10 and the others? - CORRECT ANSWER-Base10->Base2 =
Start with listing the powers of 2 from the greatest you know to least. For example: 128, 64, 32,
16, 8, 4, 2, 1. Pick the number that can fit into your number the best. So, say if your number is
75, 64 fits in the best. Then take the lesser numbers from greatest to least that fit into the
number until you have added up to your number. 8, 2, and 1 with 64 would add up to 75. Put 1's
below the numbers you needed to add up to your number and 0's over the ones that were not
used. You should end up with 1001011
, Base10->Base8 = Divide by 8 and collect the remainders starting with the last remainder to the
first, and that is your new number
Base10->Base16 = Divide by 16 and collect the remainders starting with the last remainder to
the first, and that is your new number
How can you convert between base 16 and the others? - CORRECT ANSWER-Base16->Base2 =
Take your number piece by piece. So if you had A9, you would take your A, translate it to
decimal (10), and underneath it write 8421. Circle the values that add up to 10 (8 and 2) and put
1's underneath each one you circle and 0's for the numbers you don't. You should end up with
1010. Do the same with 9. You will end up circling 8 and 1, which comes out to 1001. Put them
together, left to right, and you get your binary conversion 10101001.
Base16->Base8 = Take your number, say AC, and break it into chunks. A is 10, and C is 12. Put
8421 underneath both and circle the values that add up to A and C. If you put a 1 under the
values you circled and a 0 under the values you did not circle, you will get 0's and 1's that you
need to group into 3's. Put 421 underneath your 0's and 1's and circle the values your 1's align
with. So you should have 010 101 100, which translates to 254
Base16->Base10 = Say you have 23E. Breaking it into pieces, you will have to use 16^to the
power of each column's value starting at 0, and you multiply that by your number chunk. In our
case, we would start with E, which is 14 in decimal. So that would be 16^0 * 14, and we would
add it to every other value. 16^0 * 14 + 16^1 * 3 + 16^2 * 2, which comes out to our decimal
conversion 574.
2's complement representation of signed binary numbers - CORRECT ANSWER-the most
significant bit (leftmost digit) acts as the sign bit, where a '0' indicates a positive number and a
'1' indicates a negative number
2's complement operation - CORRECT ANSWER-To represent a negative number, you take the
binary representation of its positive counterpart, flip all the bits (one's complement), and then
add 1 to get the 2's complement representation
Identify the overflow conditions. How does it work? - CORRECT ANSWER-Add the numbers
together. The carry MostSignificantBit is the last value you carry over before the carry out,
