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

The decimal equivalent is $\boxed{13.6875_{10}}$.

$20 \div 2 = 10$ remainder 0
$10 \div 2 = 5$ remainder 0
$5 \div 2 = 2$ remainder 1
$2 \div 2 = 1$ remainder 0
$1 \div 2 = 0$ remainder 1
Reading the remainders from bottom up gives $10100_2$.

$0.6875 \times 2 = 1.375 \rightarrow 1$
$0.375 \times 2 = 0.75 \rightarrow 0$
$0.75 \times 2 = 1.5 \rightarrow 1$
$0.5 \times 2 = 1.0 \rightarrow 1$
Reading the integer parts from top down gives $0.1011_2$.

The binary equivalent is $\boxed{10100.1011_2}$.

11. (d) Using 8-bit twos complement perform the following arithmetic $25_{10} - 12_{10}$

$25_{10} = 00011001_2$

$12_{10} = 00001100_2$

Original binary: $00001100_2$
One's complement (invert bits): $11110011_2$
Two's complement (add 1 to one's complement):

So, $-12_{10}$ in 8-bit two's complement is $11110100_2$.

Discard the carry-out bit (the 9th bit) for 8-bit arithmetic.

Convert this binary result back to decimal to verify:

The result of $25_{10} - 12_{10}$ using 8-bit two's complement is $\boxed{00001101_2}$ (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.