Number System and Digits

With n binary digits, the range is 0 to 2^n - 1. For 10 bits: 2^10 - 1 = 1024 - 1 = 1023. This is the maximum unsigned value.

Only option two gives 12A7C.

¹37

19

50

20164 is the largest number formed by 4, 16, 20.

The decimal number 16 in binary is 10000, which is 5 binary digits. This is calculated by repeatedly dividing by 2: 16 = 8 remainder 0, 8 = 4 remainder 0, 4 = 2 remainder 0, 2 = 1 remainder 0, 1 = 0 remainder 1, reading remainders backwards gives 10000.

The decimal number 9 in binary is 1001, which has 4 binary digits. Converting: 9 = 4 remainder 1, 4 = 2 remainder 0, 2 = 1 remainder 0, 1 = 0 remainder 1, reading remainders backwards gives 1001.

2^-48 equals 1 divided by 2^48, which requires 48 binary fraction digits to represent. In binary, this is 0.000...001 with 47 zeros followed by a 1 at the 48th position after the decimal point.

In binary representation, the least significant bit determines parity. Odd numbers always have LSB=1 because they can be written as 2k+1, while even numbers have LSB=0 because they equal 2k.

The number of numbers which can be represented by a 10-digit binary number will be 2¹⁰ = 1024 and the numbers range from 0 - 1023. The maximum count which a 10-bit binary word can represent is 1023.

Let the ten's and unit digit be x and 8/x, respectively. Then, (10x + 8/x) + 18 = 10 x (8/x) + x 10x² + 8 + 18x = 80 + x² 9x² + 18x - 72 = 0 x² + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2. So, unit's digit = 4 and ten's digit = 2 Then, the required number is 24. Therefore, the correct answer is 24.

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let the ten's and the unit's digits be 2x and x, respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4 Required difference = (2x + x) - (2x - x) = 2x = 8 Therefore, 8 is the correct answer.

Let the middle digit be b. Then, 2b = 10 or b = 5. Let the number be abc. Now, 100 a + 10 b + c + 99 = 100 c + 10 b + a Or, a + 1 = c So, the number is  253

Let the ten's digit be x. Then, unit's digit will be x + 2. The number = 10x + (x + 2) = 11x + 2 The sum of digits = x + (x + 2) = 2x + 2 (11x + 2)(2x + 2) = 144 22x2 + 26x - 140 = 0 11x2 + 13x - 70 = 0 (x - 2)(11x + 35) = 0 x = 2 Hence, the required number = 11x + 2 = 24

Let the ten's digit be x and unit's digit be y. Then, x + y = 15 and x - y = 3 or y - x = 3. Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6. Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9. So, the number is either 96 or 69. Hence, out of the given options, option (1) is correct.  

Let the ten's digit be x and the unit's digit be y. Then, (10x + y) - (10y + x) = 36 9(x - y) = 36 x - y = 4