Build the idea
Build exam-ready understanding by connecting the core idea, formulas or facts, worked example and previous NDA questions. Focus on why each rule works, then test it under timed conditions.
Concept
Real numbers comprise rationals (terminating or recurring decimals) and irrationals (non-terminating, non-recurring). The binary system uses base 2 with digits 0 and 1; computers and several NDA questions use base conversion.
To convert decimal→binary, divide repeatedly by 2 and read remainders bottom-up; binary→decimal, multiply each digit by the place value 2ⁿ.
Key Points & Formulas
- Place values in binary: …, 16, 8, 4, 2, 1.
- Decimal→binary: successive division by 2; collect remainders in reverse.
- Binary→decimal: Σ(digit × 2^position).
- A rational number p/q is terminating only if q has prime factors 2 and/or 5 only.
Worked Example
Q. Convert the decimal number 26 to binary.
26÷2=13 r0, 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1.
Read remainders bottom to top: 11010.
Check: 16+8+0+2+0 = 26. ✓ So 26 = 11010₂.