Convert each of the following to the number system indicated: i) Convert 1101.10112 to decimal number. ii) Convert 20.687510 to binary number.

Here are the solutions to the questions. 11. (c) Convert each of the following to the number system indicated i) Convert 1101.1011_2 to decimal number. Step 1: Convert the integer part (1101_2) to decimal. 1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 1 × 2^0 = 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 8 + 4 + 0 + 1 = 13_10 Step 2: Convert the fractional part (0.1011_2) to decimal. 1 × 2^-1 + 0 × 2^-2 + 1 × 2^-3 + 1 × 2^-4 = 1 × (1)/(2) + 0 × (1)/(4) + 1 × (1)/(8) + 1 × (1)/(16) = 0.5 + 0 + 0.125 + 0.0625 = 0.6875_10 Step 3: Combine the integer and fractional parts. 13 + 0.6875 = 13.6875_10 The decimal equivalent is 13.6875_10. ii) Convert 20.6875_10 to binary number. Step 1: Convert the integer part (20_10) to binary using repeated division by 2. 20 ÷ 2 = 10 remainder 0 10 ÷ 2 = 5 remainder 0 5 ÷ 2 = 2 remainder 1 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Reading the remainders from bottom up gives 10100_2. Step 2: Convert the fractional part (0.6875_10) to binary using repeated multiplication by 2. 0.6875 × 2 = 1.375 → 1 0.375 × 2 = 0.75 → 0 0.75 × 2 = 1.5 → 1 0.5 × 2 = 1.0 → 1 Reading the integer parts from top down gives 0.1011_2. Step 3: Combine the integer and fractional parts. 10100_2 + 0.1011_2 = 10100.1011_2 The binary equivalent is 10100.1011_2. 11. (d) Using 8-bit twos complement perform the following arithmetic 25_10 - 12_10 Step 1: Convert 25_10 to 8-bit binary. 25_10 = 00011001_2 Step 2: Convert 12_10 to 8-bit binary. 12_10 = 00001100_2 Step 3: Find the two's complement of 12_10 (which represents -12_10). Original binary: 00001100_2 One's complement (invert bits): 11110011_2 Two's complement (add 1 to one's complement): 11110011_2 + 1_2 = 11110100_2 So, -12_10 in 8-bit two's complement is 11110100_2. Step 4: Perform the addition 25_10 + (-12_10). 00011001_2 (25_10) + 11110100_2 (-12_10) 2.5cm0.4pt 100001101_2 Discard the carry-out bit (the 9th bit) for 8-bit arithmetic. Step 5: The 8-bit result is 00001101_2. Convert this binary result back to decimal to verify: 0 × 2^7 + 0 × 2^6 + 0 × 2^5 + 0 × 2^4 + 1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 1 × 2^0 = 0 + 0 + 0 + 0 + 8 + 4 + 0 + 1 = 13_10 The result of 25_10 - 12_10 using 8-bit two's complement is 00001101_2 (which is 13_10). 20. (a) Distinguish between formatting a disk and partitioning a disk with reference to the operating system. Partitioning a disk is the process of dividing a physical hard drive into one or more logical sections, called partitions. Each partition acts as an independent storage unit, allowing the operating system to treat them as separate drives (e.g., C:, D:). Partitioning defines the structure* of the disk. Formatting a disk (or a partition) is the process of preparing it for use by an operating system by creating a file system (e.g., NTFS, FAT32). This file system organizes how data is stored and retrieved. Formatting typically erases all existing data on the selected partition or disk. Formatting defines how data is stored* within a partition. 3 done, 2 left today. You're making progress.