Number System – 9

Number System – Exercise – 1 (Answer)

1. Divisor = 41, dividend = 15625, quotient = 381 and remainder = 4.

2. Divisor = (dividend – remainder )/quotient = (397246 – 211)/865 = 459.

3. Divisor = (dividend – remainder )/quotient = (x + ak) – x/a = k.

4. On dividing 87375 by 698, the remainder is 125, the least number to be subtracted from the dividend in the remainder

So, the least number to be subtracted = 125.

5. On dividing 49123 by 263, the remainder is 205, the least number to be added to the dividend = divisor – remainder = 263 – 205 = 58.

So, the least number to be added = 58.

6. The greatest 3 digit number = 999, on dividing 999 by 35, remainder = 19.

So, the required number = dividend – remainder = 999 – 19 = 980.

7. The least number of 3-digits = 100. On dividing 100 by 14, remainder = 2

So, the required number = dividend + (divisor – remainder) = 100 + (14 – 2) = 112.

8. Here, the divisor 602 is multiple of the divisor 14, and greater divisor remainder is greatest then smaller divisor.

So, required number = 34/14 = 8.

9. Here, the divisor 357 is the multiple of the divisor 17, but the greater divisor remainder is smaller then smaller divisor,

So, the remainder is same which is 5.

10. The binary equivalent of these number is:-

(i) (30)¹⁰ = (11110)²

(ii) (27)¹⁰ = (11011)²

(iii) (41)¹⁰ = (101001)²