Difference between revisions of "CSC103 Homework 1 2012f"
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| − | This homework | + | This homework assignment is''' due''' on '''Thursday Sept. 20th, at 9:00 a.m'''. Please print it or write it on paper, and bring it to class on the due date. |
| − | < | + | <font color="#ff0000">No late assignments will be accepted.</font> |
| − | |||
</tanbox> | </tanbox> | ||
| − | < | + | |
| − | < | + | =Question #1= |
| − | + | ||
| − | < | + | Count in binary and write down first 33 numbers of the series. In other words, complete the second column in the list below. |
| − | </ | + | |
| − | < | + | Decimal Binary |
| + | 0 0 | ||
| + | 1 1 | ||
| + | 2 10 | ||
| + | 3 11 | ||
| + | 4 ... | ||
| + | 5 | ||
| + | 6 | ||
| + | 7 | ||
| + | 8 | ||
| + | 9 | ||
| + | 10 | ||
| + | 11 | ||
| + | 12 | ||
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| + | 14 | ||
| + | 15 | ||
| + | 16 | ||
| + | 17 | ||
| + | 18 | ||
| + | 19 | ||
| + | 20 | ||
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| + | 23 | ||
| + | 24 | ||
| + | 25 | ||
| + | 26 | ||
| + | 27 | ||
| + | 28 | ||
| + | 29 | ||
| + | 30 | ||
| + | 31 | ||
| + | 32 | ||
| + | |||
| + | Perform the following additions in binary: | ||
| + | |||
| + | <code><pre> | ||
| + | |||
| + | 10011 + 10011 = | ||
| + | |||
| + | 10111 + 00110 = | ||
| + | |||
| + | </pre></code> | ||
| + | |||
| + | =Question #2= | ||
| + | |||
| + | Assume that we live in a universe where everybody only has 4 fingers. Just as we did in class with a system of 2 digits (binary code), we invente a system for counting with only 4 digits: 0, 1, 2, and 3. | ||
| + | |||
| + | * Write the first 20 numbers of a system with 4 digits. To help you out, I will start with the first 7 numbers of the series: | ||
| + | |||
| + | 0 | ||
| + | 1 | ||
| + | 2 | ||
| + | 3 | ||
| + | 10 | ||
| + | 11 | ||
| + | 12 | ||
| + | ... | ||
| + | |||
| + | Continue on until you have 20 consecutive numbers of a system in base 4. | ||
| + | |||
| + | =Question #3= | ||
| + | |||
| + | Perform the addition of the following numbers in base 4. | ||
| + | |||
| + | <code><pre> | ||
| + | |||
| + | 1002 + 2301 = | ||
| + | |||
| + | 2222 + 3301 = | ||
| + | |||
| + | </pre></code> | ||
| + | |||
| + | |||
| + | =Question #4= | ||
| + | |||
| + | Assume that we have several boolean expressions, labeled E1 to E6: | ||
| + | |||
| + | * E1: is a Smith student | ||
| + | * E2: is a senior | ||
| + | * E3: likes vanilla | ||
| + | * E4: has class on Monday | ||
| + | * E5: is a Hampshire student | ||
| + | * E6: is on the crew team | ||
| + | |||
| + | What is the boolean expression that is a combination of E1, E2, E3, E4, and/or E5, and the logic operators AND, OR, and NOT, that will be True whenever I find somebody on campus who is a Hamshire College student and who does not like vanilla? | ||
| + | |||
| + | '''Hints''': | ||
| + | # ''see if you can discard any of the boolean expressions, and write the truth table for the wanted expression.'' | ||
| + | # ''generating the truth table for what you want will help you get the boolean expression.'' | ||
| + | |||
| + | <br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /> | ||
<br /> | <br /> | ||
[[Category:CSC103]][[Category:Homework]] | [[Category:CSC103]][[Category:Homework]] | ||
Latest revision as of 09:21, 13 September 2012
--D. Thiebaut 07:53, 11 September 2012 (EDT)
This homework assignment is due on Thursday Sept. 20th, at 9:00 a.m. Please print it or write it on paper, and bring it to class on the due date. No late assignments will be accepted.
Question #1
Count in binary and write down first 33 numbers of the series. In other words, complete the second column in the list below.
Decimal Binary 0 0 1 1 2 10 3 11 4 ... 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Perform the following additions in binary:
10011 + 10011 =
10111 + 00110 =
Question #2
Assume that we live in a universe where everybody only has 4 fingers. Just as we did in class with a system of 2 digits (binary code), we invente a system for counting with only 4 digits: 0, 1, 2, and 3.
- Write the first 20 numbers of a system with 4 digits. To help you out, I will start with the first 7 numbers of the series:
0 1 2 3 10 11 12 ...
Continue on until you have 20 consecutive numbers of a system in base 4.
Question #3
Perform the addition of the following numbers in base 4.
1002 + 2301 =
2222 + 3301 =
Question #4
Assume that we have several boolean expressions, labeled E1 to E6:
- E1: is a Smith student
- E2: is a senior
- E3: likes vanilla
- E4: has class on Monday
- E5: is a Hampshire student
- E6: is on the crew team
What is the boolean expression that is a combination of E1, E2, E3, E4, and/or E5, and the logic operators AND, OR, and NOT, that will be True whenever I find somebody on campus who is a Hamshire College student and who does not like vanilla?
Hints:
- see if you can discard any of the boolean expressions, and write the truth table for the wanted expression.
- generating the truth table for what you want will help you get the boolean expression.
