Data Formats and Arithmetic Operations for each Format

Book Section 2.1.

Rather than accessing individual bits in memory, most computers use blocks of 8 bits, or bytes, as the smallest addressable unit of memory. A machine-level program views memory as a very large array of bytes, referred to as virtual memory. Every byte of memory is identified by a unique number, known as its address, and the set of all possible addresses is known as the virtual address space. As indicated by its name, this virtual address space is just a conceptual image presented to the machine-level program. The actual implementation is by use of combination of dynamic random access memory (DRAM).

Hexadecimal Notation:

A single byte consists of 8 bits. In binary notation, its value ranges from 00000000₂ to 11111111₂. When viewed as a decimal integer, its value ranges from 0₁₀ to 255₁₀. Hexadecimal (or simply “hex”) uses digits ‘0’ through ‘9’ along with characters ‘A’ through ‘F’ to represent 16 possible values. Written in hexadecimal, the value of a single byte can range from 00₁₆ to FF₁₆. In C, numeric constants starting with 0x or 0X are interpreted as being in hexadecimal. The characters ‘A’ through ‘F’ may be written in either upper- or lowercase. For example, we could write the number FA1D37B16 as 0xFA1D37B, as 0xfa1d37b, or even mixing upper- and lowercase (e.g., 0xFa1D37b).

Conversion between Different Number Systems:

Decimal	Hexa-Decimal	Binary
0	0	0000
1	1	0001
2	2	0010
3	3	0011
4	4	0100
5	5	0101
6	6	0110
7	7	0111
8	8	1000
9	9	1001
10	A	1010
11	B	1011
12	C	1100
13	D	1101
14	E	1110
15	F	1111

Number Conversion for Different Bases

Exercise, book 2.1:

Perform the following number conversions:

1. 0x25B9D2 to binary
2. binary 1010111001001001 to hexadecimal
3. 0xA8B3D to binary
4. binary 1100100010110110010110 to hexadecimal

Exercise, Book 2.2:

n	2n (Decimal)	2n (Hexadecimal)
5	32	0x20
23	8388608	0x800000
15	32768	0x8000
13	8192	0x2000
12	4096	0x1000
6	64	0x40
8	256	0x100

Exercise, Book 2.2

Exercise, Book 2.3:

Decimal	Binary	Hexadecimal
0	00000000	0x00
158	10011110	0x9E
76	01001100	0x4C
145	10010001	0x91
174	10101110	0xAE
60	00111100	0X3C
361	11110001	0XF1
43981	1010101111001101	0xabcd
123	01111011	0x7B
117	01110101	0x75
189	10111101	0xBD
245	11110101	0xF5

Exercise, Book 2.3

Exercise, Book 2.4:

Solve below subtraction and addition operations.

1. 0x605c – 0x5 = _______________________
2. 0x605c – 0x20 = ______________________
3. 0x605c + 32 = _______________________
4. 0x60fa – 0x601fc = __________________

Boolean/Logical Operations:

Operations (bit wise) are ~, &, | , and ^ encode logical operations for not, and, or, and exclusive-or, respectively

1. AND operation: 0110 & 1100 = 0100
2. OR Operation: 0110 | 1100 = 1110
3. Exclusive-OR Operation: 0110 ^ 1100 = 1010
4. NOT Operation: ~0110 = 1001

Bit Level Operations:

C Expression	Binary Expression	Binary Result	Hexadecimal Result
~0x41	~ 01000001	10111110	0xBE
~0x00	~ 00000000	11111111	0xFF
0x69 & 0x55	01101001 & 01010101	01000001	0x41
0x69 | 0x55	01101001 | 01010101	01111101	0x7D

Bit wise operations

Shifting operations: Book 2.1.9

Exercise, Book 2.16:

Operations	Value 1	Value 2
Argument x	01100011	10010101
x << 4	00110000	01010000
x >> 4	00000110	00001001
x >> 4 (Arithmetic)	00000110	11111001

Shifting operations

Do following exercise by yourself.

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