Addition, Subtraction & Multiplication | Algebra - Number System
Add (1101)2 and (101)2. Write your answer in base 2.
Answer: 10010
Explanation :
When we add numbers in non-decimal system, add them as we do in decimal system but write them according to the given base system.
Step 1: Adding unit’s digits.
Add them as decimal system i.e., 1 + 1 = 2.
Now write 2 in binary system i.e., (2)10 = (11)2
Write 0 and carry over 1 as we do with normal addition.
Step 2: Adding ten’s digits.
Add them as decimal system i.e., 1 + 0 + 0 = 1.
Step 3: Adding hundred’s digits.
Add them as decimal system i.e., 1 + 1 = 2.
Now write 2 in binary system i.e., (2)10 = (10)2
Write 0 and carry over 1.
Step 4: Adding thousand’s digits.
Add them as decimal system i.e., 1 + 1 = 2.
Now write 2 in binary system i.e., (2)10 = (10)2
Hence, 10010.
Workspace:
Add (1034)5 and (210)5. Write your answer in base 5.
Answer: 1244
Explanation :
When we add numbers in non-decimal system, add them as we do in decimal system but write them according to the given base system.
Step 1: Adding unit’s digits.
Step 2: Adding ten’s digits.
Step 3: Adding hundred’s digits.
Step 4: Adding thousand’s digits.
Hence, 1244.
Workspace:
Add (1357)8 and (2672)8. Write your answer in base 8.
Answer: 4251
Explanation :
When we add numbers in non-decimal system, add them as we do in decimal system but write them according to the given base system.
Step 1: Adding unit’s digits, 7 + 2 = 9 = (11)8
Step 2: Adding ten’s digits, 1 + 5 + 7 = 13 = (15)8
Step 3: Adding hundred’s digits, 1 + 3 + 6 = 10 = (12)8
Step 4: Adding thousand’s digits, 1 + 1 + 2 = 4 = (4)8
Hence, 4251.
Workspace:
Calculate (1101)2 - (101)2. Write your answer in base 2.
Answer: 1000
Explanation :
When we subtract numbers in non-decimal system, subtract them as we do in decimal system but write them according to the given base system.
Step 1: Subtracting unit’s digits.
Subtract them as decimal system i.e., 1 - 1 = 0.
Step 2: Subtracting ten’s digits.
Subtract them as decimal system i.e., 0 + 0 = 0.
Step 3: Subtracting hundred’s digits.
Subtract them as decimal system i.e., 0 - 0 = 0.
Step 4: Subtracting thousand’s digits.
Subtract them as decimal system i.e., 1 - 0 = 1.
Hence, 1000.
Workspace:
Calculate (100)2 - (11)2. Write your answer in base 2.
Answer: 1
Explanation :
When we subtract numbers in non-decimal system, subtract them as we do in decimal system but write them according to the given base system.
Step 1: Subtracting unit’s digits.
When we subtract bigger number from a smaller number, we borrow from the left of the smaller digit.
Since we are dealing in base 2, when we borrow, we subtract 1 from the left digit and add 2 in the smaller digit.
Now subtract as we do in decimal system i.e., 2 + 0 – 1 = 1
Step 2: Subtracting ten’s digits.
When we subtract bigger number from a smaller number, we borrow from the left of the smaller digit.
Since we are dealing in base 2, when we borrow, we subtract 1 from the left digit and add 2 in the smaller digit.
Now subtract as we do in decimal system i.e., 2 – 1 + 0 - 1 = 0.
Step 3: Subtracting hundred’s digits.
Subtract as we do in decimal system i.e., -1 + 1 – 0 = 0.
Hence, 1.
Workspace:
Calculate (235)8 - (66)8. Write your answer in base 8.
Answer: 147
Explanation :
When we subtract numbers in non-decimal system, subtract them as we do in decimal system but write them according to the given base system.
Step 1: Subtracting unit’s digits.
When we subtract bigger number from a smaller number, we borrow from the left of the smaller digit.
Since we are dealing in base 8, when we borrow, we subtract 1 from the left digit and add 8 in the smaller digit.
Now subtract as we do in decimal system i.e., 8 + 5 – 6 = 7.
Step 2: Subtracting ten’s digits.
When we subtract bigger number from a smaller number, we borrow from the left of the smaller digit.
Since we are dealing in base 8, when we borrow, we subtract 1 from the left digit and add 8 in the smaller digit.
Now subtract as we do in decimal system i.e., 8 – 1 + 3 – 6 = 4.
Step 3: Subtracting hundred’s digits.
Now subtract as we do in decimal system i.e., – 1 + 2 = 1.
Hence, 147.
Workspace:
Multiply (22)3 and (22)3. Write your answer in base 3.
Answer: 2101
Explanation :
When we multiply numbers in non-decimal system, multiply them as we do in decimal system but write them according to the given base system.
Step 1: Multiplying unit’s digits.
Multiply them as decimal system i.e., 2 × 2 = 4.
Now write 4 in base 3 i.e., (4)10 = (11)3
Write 1 and carry over 1 as we do with normal multiplication.
Step 2: Multiplying unit’s and ten’s digits.
Multiply them as decimal system i.e., 2 × 2 + 1 = 5.
Now write 5 in base 3 i.e., (5)10 = (12)3
Step 3: Multiplying ten’s and unit’s digits.
Multiply them as decimal system i.e., 2 × 2 = 4.
Now write 4 in base 3 i.e., (4)10 = (11)3
Step 4: Multiplying ten’s digits.
Multiply them as decimal system i.e., 2 × 2 + 1= 5.
Now write 5 in base 3 i.e., (5)10 = (12)3
Step 5: Add the two results obtained.
∴ (22)3 × (22)3 = (2101)3.
Hence, 2101.
Workspace:
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