Every answer below is checked by
labs/course-1-office/unit1_number_systems.py, which fails if any conversion
on this page is wrong.
Q1
Decimal: 128 + 64 + 0 + 16 + 0 + 4 + 2 + 0 = 214
Octal — group in threes from the right: 011 | 010 | 110 → 3, 2, 6 →
(326)₈
Hexadecimal — group in fours from the right: 1101 | 0110 → D, 6 →
(D6)₁₆
Check: 13 × 16 + 6 = 208 + 6 = 214 ✓
Q2
Binary — divide by 2 repeatedly: 2024→1012 r0, 1012→506 r0, 506→253 r0, 253→126 r1, 126→63 r0, 63→31 r1, 31→15 r1, 15→7 r1, 7→3 r1, 3→1 r1, 1→0 r1
Reading upwards: (11111101000)₂
Hexadecimal — group the binary in fours: 0111 | 1110 | 1000 → 7, E, 8 →
(7E8)₁₆
Check: 7 × 256 + 14 × 16 + 8 = 1792 + 224 + 8 = 2024 ✓
Octal — group in threes: 011 | 111 | 101 | 000 → 3, 7, 5, 0 →
(3750)₈
Check: 3 × 512 + 7 × 64 + 5 × 8 + 0 = 1536 + 448 + 40 = 2024 ✓
Q3
Decimal: A(10) × 256 + 7 × 16 + C(12) × 1 = 2560 + 112 + 12 = 2684
Binary: A → 1010, 7 → 0111, C → 1100 → (101001111100)₂
Octal — regroup the binary in threes: 101 | 001 | 111 | 100 → 5, 1, 7, 4
→ (5174)₈
Check: 5 × 512 + 1 × 64 + 7 × 8 + 4 = 2560 + 64 + 56 + 4 = 2684 ✓
Q4
Multiply by 2 and read the integer parts downwards:
| Step | Result | Integer |
|---|---|---|
| 0.6875 × 2 | 1.375 | 1 |
| 0.375 × 2 | 0.75 | 0 |
| 0.75 × 2 | 1.5 | 1 |
| 0.5 × 2 | 1.0 | 1 |
(0.1011)₂
Check: 0.5 + 0 + 0.125 + 0.0625 = 0.6875 ✓
Q5
110110 (54)
- 010111 (23)
--------
011111 (31)
Check: 54 − 23 = 31, and 011111 = 16 + 8 + 4 + 2 + 1 = 31 ✓
Q6
The number is 64 + 32 + 8 + 1 = 105.
1's complement — flip every bit: 10010110
2's complement — add 1 to that: 10010111
Check: 01101001 + 10010111 = 100000000; the ninth bit overflows out of 8
bits, leaving 00000000 ✓
Q7. Why do computers use binary rather than decimal?
A transistor has two stable states — conducting or not — so two symbols map directly onto the hardware. A decimal system would need ten distinguishable voltage levels, which is far harder to build reliably and far more susceptible to noise. Binary also makes arithmetic circuits simple, since Boolean algebra maps directly onto logic gates.
Q8. Distinguish the ALU from the CU.
The ALU performs the actual arithmetic (+, −, ×, ÷) and logical (AND, OR, NOT, comparison) operations. The CU performs no computation at all — it fetches instructions, decodes them, and generates the control signals that tell every other unit what to do and when. Together with registers they make up the CPU.
Q9. Why is 2's complement preferred over sign–magnitude?
Three reasons: subtraction becomes addition, so one circuit does both; there is only one representation of zero (sign–magnitude has +0 and −0); and the range is slightly wider — 8 bits give −128 to +127 rather than −127 to +127.
Q10. Distinguish a hub from a switch.
A hub operates at the physical layer and broadcasts every incoming frame to every port, so bandwidth is shared and collisions occur. A switch operates at the data link layer, learns which MAC address is on which port, and forwards the frame only to the correct port — giving each connection full bandwidth and no collisions.
Q11. Why does a "500 GB" hard disk show as about 465 GB?
The manufacturer uses decimal units: 500 GB = 500,000,000,000 bytes. The operating system divides by 1024 three times, giving 500 × 10⁹ / 1024³ ≈ 465. Nothing is missing; the two are counting in different bases.
Q12. Differentiate a transition from an animation.
DEFINITION
A transition is the effect when moving from one slide to the next (Transitions tab). An animation is the effect applied to an object within a slide — text flying in, a chart building (Animations tab).
Q13
Marks are in column B. Assign A ≥ 90, B ≥ 75, C ≥ 60, D ≥ 40, otherwise F.
=IF(B2>=90,"A", IF(B2>=75,"B", IF(B2>=60,"C", IF(B2>=40,"D","F"))))
Order matters — the highest threshold must be tested first. Reversing the
ladder gives every passing student a D, because >=40 is true for all of them
and the first true condition wins.
Excel 2019+ alternative:
=IFS(B2>=90,"A", B2>=75,"B", B2>=60,"C", B2>=40,"D", TRUE,"F")
Q14
IDs in A2:A100, names in B, departments in C, salaries in D. The ID to look up is in F2.
=VLOOKUP(F2, $A$2:$D$100, 4, FALSE)
$A$2:$D$100 — anchored, so copying the formula down does not shift the table4 — the fourth column of the table array, which is column DFALSE — exact match; omitting it defaults to approximate and gives silently
wrong answersWrapped against a missing ID:
=IFERROR(VLOOKUP(F2,$A$2:$D$100,4,FALSE), "Employee not found")
The modern equivalent, which can look leftwards and needs no IFERROR:
=XLOOKUP(F2, $A$2:$A$100, $D$2:$D$100, "Employee not found")
Q15
Full name in A2, e.g. Ananya Sharma.
First name: =LEFT(A2, FIND(" ",A2)-1)
Last name: =RIGHT(A2, LEN(A2)-FIND(" ",A2))
FIND(" ",A2) returns 7 for Ananya Sharma. So LEFT(A2,6) gives Ananya,
and RIGHT(A2, 13-7) = RIGHT(A2,6) gives Sharma.
Wrap it in IFERROR for names with no space, or FIND returns #VALUE!.
Q16
| Task | Formula |
|---|---|
| How many scored above 75 | =COUNTIF(B2:B50, ">75") |
| How many in IT scoring above 75 | =COUNTIFS(A2:A50,"IT", B2:B50,">75") |
| Total salary of the IT department | =SUMIF(A2:A50, "IT", C2:C50) |
| Average salary in IT | =AVERAGEIF(A2:A50, "IT", C2:C50) |
Note the argument order: SUMIF(range, criteria, sum_range) but
SUMIFS(sum_range, range1, criteria1, …).
Q17
A2:F50Conditional Formatting → New Rule → Use a formula to determine which cells to format
Enter =$C2<40
The reference must be $C2. The $ locks the column so every cell in the
row is tested against column C, while the relative row number lets each row test
its own value. $C$2 would test every row against one cell; C2 would test
each cell against the column beside it.
Q18
A budget sheet computes savings in B10 from income (B2) and expenses. Savings currently show ₹4,000; you want ₹12,000.
Data → What-If Analysis → Goal Seek:
| Field | Value |
|---|---|
| Set cell | B10 (the savings formula) |
| To value | 12000 |
| By changing cell | B2 (income) |
Goal Seek adjusts income until savings reach 12,000 and reports the value required.
The changing cell must contain a value, not a formula — Goal Seek can only adjust an input, not a calculated result.
Q19
Give a table with generation, years, technology, languages and examples, then a paragraph on each generation's characteristics, then the overall trend — smaller, faster, cheaper, more reliable, lower power.
Full treatment in unit-1.md §1.4.
Q20
Draw bus, star and ring. For each give the structure, advantages and disadvantages. Then state which is dominant today and why — star, because every switched Ethernet network is physically a star, and a single node failing does not affect the rest.
Add the mesh cable-count formula, n(n−1)/2, if the question mentions mesh.
Q21
Cover the four areas (Rows, Columns, Values, Filters), creation, value settings, grouping and refreshing. Then explain slicers and Report Connections — one slicer driving several pivot tables is what makes a dashboard interactive rather than a set of static charts.
Finish with the layout and design principles from unit-5.md §5.6.
$ do in a cell reference?Answers: 1. 10; 1010. · 2. 4 and 8. · 3. The Control Unit. · 4. Primary is
directly accessible to the CPU and mostly volatile; secondary is slower,
non-volatile, and reached only through primary. · 5. Bus, star, ring. ·