1. Number Systems and Bitwise Operation
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

2. DKT121: Fundamental of Computer Programming
Binary, Octal, Hexadecimal, and Decimal
Binary
Binary numbering system has only two possible values for each digit: 0 and 1.
For example,
binary number decimal number
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

3. DKT121: Fundamental of Computer Programming
Decimal Numbers
Decimal
The digits' weight increases by powers of 10. The weighted values for
each position is determined as follows:
104
103
102
101
100
10000
1000 10 1
For example,
A decimal number 4261 can be thought of as follows.
4 * * * * 1 =
= 4261 (decimal)
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

4. Binary, Octal, Hexadecimal, and Decimal
The digits' weight increases by powers of 2. The weighted values for each position is
determined as follows: 27 26 25 24 23 22 21 20
128 64 32 16 8 4 2 1
For example,
binary 10 is decimal 2.
the binary value represents the decimal value 202.
1 * * * * * * * * 1 =
= 202 (decimal)
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

5. Binary Two’s Complement
The left-most bit is the sign bit. If it is 1, then the number is negative.
Otherwise, it is positive. Give a negative value, represent it in binary two’s
complement form as follows.
write the number in its absolute value.
complement the binary number.
plus 1.
Example, represent –2 in binary two’s complement with 16 bits for short int.
Binary value of 2: b
Binary complement of 2: b
Plus 1:
Binary two’s complement representation of -2: 0b
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

6. DKT121: Fundamental of Computer Programming
Give binary two’s complement form of a negative number, find
the absolute value of the negative value as follows.
Complement the binary number.
Plus 1.
Example, find the decimal value of (0b )2 in binary
two’s complement form with 16 bits.
Binary two’s complement (0b )2
Binary complement (0b )2
Plus
Absolute value: (0b )2 = 210
Negative value:
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

7. DKT121: Fundamental of Computer Programming
Subtraction of a value in the computer can be treated as addition of its
two’s complement. For example, the subtraction of (2-2) can be
performed as 2+(-2) as follows:
0b (binary representation of 2)
0b (two’s complement representation of -2)
0b (2+(-2))
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

8. DKT121: Fundamental of Computer Programming
Example
> short i, j
> i = 0b 2
> j = 0b -2
> i+j
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

9. DKT121: Fundamental of Computer Programming
Octal
The octal system is based on the binary system with a 3-bit boundary. The octal
number system uses base 8 includes 0 through 7. The weighted values for each
position is as follows: 83 82 81 80
512 64 8 1
Binary to Octal Conversion
Break the binary number into 3-bit sections from the least significant bit (LSB) to the most significant bit (MSB).
Convert the 3-bit binary number to its octal equivalent.
For example, the binary value equals to
octal value ( )8.
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

10. DKT121: Fundamental of Computer Programming
Octal to Binary Conversion
Convert the octal number to its 3-bit binary equivalent.
Combine all the 3-bit sections.
For example, the octal value equals to binary value
Octal to Decimal Conversion
To convert octal number to decimal number, multiply the value in each position
by its octal weight and add each value together. For example, the octal value
(167)8 represents decimal value 119.
1*64 + 6*8 + 7*1 = 119
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

11. DKT121: Fundamental of Computer Programming
Hexadecimal
Similar to octal, the hexadecimal system is also based on the binary system but
using 4-bit boundary. The hexadecimal number system uses base 16 including
the digits 0 through 9 and the letters A, B, C, D, E, and F. The letters A through F
represent the decimal numbers 10 through 15. For the decimal values from 0 to 15,
the corresponding hexadecimal values are listed below. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 F E D C B A
Decimal
Hexadecimal
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

12. DKT121: Fundamental of Computer Programming
The weighted values for each position is as follows:
163
162
161
160
4096
256 16 1
The conversion between binary value and hexadecimal value is similar to octal
number,but using four-bit sections.
The hexadecimal value 20A represents decimal value 522.
2* * *1 = 522
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

13. DKT121: Fundamental of Computer Programming
Following table provides all the information you need to convert from one type
number into any other type number for the decimal values from 0 to16.
Binary
Octal
Decimal
Hex
0000 00
1001 11 09
0001 01
1010 12 10 A
0010 02
1011 13 B
0011 03
1100 14 C
0100 04
1101 15 D
0101 05
1110 16 E
0110 06
1111 17 F
0111 07
10000 20
1000 08
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

14. DKT121: Fundamental of Computer Programming
Bitwise Operators
There are six bitwise operators:
Operator
Name
Description
&
bitwise AND
The bit is set to 1 if the corresponding bits in the two operands are both 1. |
bitwise OR
The bit is set to 1 if at least one of the corresponding bits in the two operands is 1. ^
bitwise exclusive OR
The bit is set to 1 if exactly one of the corresponding bits in the two operands is 1.
<<
left shift
Shift the bits of the first operand left by the number of bits specified by the second operand; fill from right with 0 bits.
>>
right shift
Shift the bits of the first operand right by the number of bits specified by the second operand; filling from the left is implementation dependent. ~
One’s complement
Set all 0 bits to 1, and all 1 bits to 0.
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

15. DKT121: Fundamental of Computer Programming
Example: a b
a & b
a | b
a ^ b
b << 1
a >> 1 ~a
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

16. DKT121: Fundamental of Computer Programming
/* File: bitop.ch (run in Ch only)
Use Ch features “%b” and 0b */
#include <stdio.h>
int main() {
char a = 0b ;
char b = 0b ;
char c;
printf("a = b%8b\n", a);
printf("b = b%8b\n", b);
c = a & b;
printf("a & b = 0b%8b\n", c);
c = a | b;
printf("a | b = 0b%8b\n", c);
c = a ^ b;
printf("a ^ b = 0b%8b\n", c);
c = b << 1;
printf("b << 1 = 0b%8b\n", c);
c = a >> 1;
printf("a >> 1 = 0b%8b\n", c);
c = ~a;
printf("~a = 0b%8b\n", c);
return 0; }
Output:
a = b
b = b
a & b = 0b
a | b = 0b
a ^ b = 0b
b << 1 = 0b
a >> 1 = 0b
~a = 0b
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming

17. DKT121: Fundamental of Computer Programming
Logic Operators
There are four logic operators:
1) ! logic NOT
2) && --- logic AND
3) || inclusive OR
4) ^^ exclusive OR (available in Ch only) a b !a
a && b
a || b
a ^^ b 1
UniMAP Sem2-09/10
DKT121: Fundamental of Computer Programming