Are these Numbers notes free?

Yes. The full 4-page Numbers sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Numbers revision sheet cover?

A base is a promise about place value, The four bases the paper uses, Binary, base 2, Octal, base 8, Decimal, base 10, Hexadecimal, base 16, Reading any base back into decimal, positional expansion, worked, binary, worked, hexadecimal, Decimal into any base, by repeated division, Divide.

Is this for Class 11 ISC Computer Science?

Yes, it is written for the ISC Computer Science syllabus.

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Numbers — Class 11 ISC Computer Science revision notes

A 4-page visual revision sheet for Numbers, written for Class 11 ISC Computer Science. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Numbers revision notes, page 1 of 4 — Page 1 of 4. The remaining 3 pages open in the app.

Numbers in one look

counting in four bases, and the complement trick that turns subtraction into addition

A base is a promise about place value

in any base b, the digit sitting k places left of the point is worth b to the power k, and the digits allowed run from 0 up to b minus 1
so base 2 allows only 0 and 1, base 8 allows 0 to 7, base 10 allows 0 to 9, and base 16 allows 0 to 9 then A B C D E F for ten to fifteen
the same written symbols mean different numbers in different bases: 10 is two in binary, eight in octal, sixteen in hexadecimal
write the base as a subscript whenever there is any doubt, because a bare 110 is ambiguous and an examiner will read it as decimal

The four bases the paper uses

Binary, base 2: digits 0 and 1, the machine's own representation, every other base here is a convenience for humans reading it
Octal, base 8: digits 0 to 7, one octal digit stands for exactly three bits
Decimal, base 10: digits 0 to 9, the base every answer is finally checked against
Hexadecimal, base 16: digits 0 to 9 then A to F, one hex digit stands for exactly four bits

Reading any base back into decimal

positional expansion N = d_n b^n + d_n-1 b^n-1 + ... + d_1 b^1 + d_0 b^0
worked, binary 1011_2 = 1(8) + 0(4) + 1(2) + 1(1) = 11_10
worked, hexadecimal 2F_16 = 2(16) + 15(1) = 47_10

Page 1 of 4. The full sheet, all 4 pages, opens free in the app.

What this Numbers sheet covers

A base is a promise about place value
The four bases the paper uses
Binary, base 2
Octal, base 8
Decimal, base 10
Hexadecimal, base 16
Reading any base back into decimal
positional expansion
worked, binary
worked, hexadecimal
Decimal into any base, by repeated division
Divide
Note the remainder
Repeat
Read upward
Grouping bits is faster than dividing
Worked: subtracting by 2's complement
Octal against hexadecimal
Octal
Hexadecimal
The two complements, from the same bit pattern
1's complement
2's complement
worked on 4 bits
Subtracting with 1's against 2's complement
1's complement method
2's complement method
Words the question will use
Why the machine prefers 2's complement
Adding in binary is four facts and a carry
Traps that cost marks
Tricks that save time

Open the full Numbers sheet →Free, works offline, no account needed. All 4 pages, plus a study plan built around your own exam dates.

How CapCompass uses this sheet

These notes are not a standalone PDF. CapCompass plans Computer Science chapter by chapter against your real exam dates and free hours, and when the plan reaches Numbers the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.