Decimal and Binary Systems
decimal or denary system, namely system
numbers with a base 10, which has 10 pieces of symbols, ie 0,1,2 ... 9. While the binary system is base 2 number system, and has only two symbols ie 0
and 1. Here is a comparison of the decimal and binary number system.
Decimal System
Base (Radix): 10
Absolute Digit: 0,1,2 ... 9
Positional Value: ... 102 101 100 10-1 10-2 ...
Example:
743.15 = 7 * 102 + 4 * 101 + 3 * 100 + 1 * 10-1 + 5 * 10-2
Operating in a computer is done in a binary system.
Base (Radix): 2
Absolute Digit: 0.1
Positional Value: ... 22 21 20 2-1 2-2 ...
Example:
00110 = 0 * 24 + 0 * 23 + 1 * 22 + 1 * 21 + 0 * 20
Octal number system
Base (Radix): 8
Absolute Digit: 0,1,2 ... 7
Positional Value: ... 82 81 80 8-1 8-2 ...
Octal number system is based on 8 and has eight symbols
Different numbers 0,1,2 ... 7. In an octal number can be described in
exponent base 8.
System Hexadecimal Numbers
Base (Radix): 16
Absolute Digit: 0,1,2 ... 9, A, B, C, D, E, F
Positional Value: 162 161 160 16-1 ... 16-2 ...
Example:
Convert to decimal numbers 110 112
110112 = 24 + 23 + 21 + 20
= 16 + 8 + 2 + 1
= 2710
Convert 7568 to decimal numbers
7568 = 7 * 82 + 5 * 81 + 6 * 80
= 448 + 40 + 6
= 49 410
Convert to decimal number 31A16
31A16 = 3 * 162 + 1 * 161 + 10 * 160
= 768 + 16 + 10
= 79 410
Conversion from one number system to decimal number system
Convert to decimal numbers 110 112
110112 = 24 + 23 + 21 + 20
= 16 + 8 + 2 + 1
= 2710
Conversion to a binary number system octal number system
10110111.1011102
we will classify the three-three:
010 110 111, 101 1102 = 267.568
Conversion to the octal number system binary number system
Formula:
Return the octal value in accordance with the corresponding binary value
Example:
745.238 = 111 100 101, 010 0112
= 111,100,101.0100112
Converting the binary number system to hexadecimal number system
Formula:
• Group the four-four.
• If less than four given a 0 in front for the numbers in front of the comma and the
back to numbers after the decimal point.
Example:
1011110111.011010002
we will classify the four-four:
0010 1111 0111, 0110 10002 = 2F7, 6816
Converting hexadecimal number system into binary number system
Formula:
Return the hex value in accordance with the corresponding binary values (see table)
Example:
ABC, DE16 = 1010 1011 1100 1110 11 112
= 101,010,111,100.111011112
Table Converting hexadecimal numbers to binary
Hexadecimal Binary Hexadecimal Binary
0 0000 8 1000
1 0001 9 1001
2 0010 A 1010
3 0011 B 1011
4 0100 C 1100
5 0101 D 1101
6 0110 E 1110
7 0111 1111 F
decimal or denary system, namely system
numbers with a base 10, which has 10 pieces of symbols, ie 0,1,2 ... 9. While the binary system is base 2 number system, and has only two symbols ie 0
and 1. Here is a comparison of the decimal and binary number system.
Decimal System
Base (Radix): 10
Absolute Digit: 0,1,2 ... 9
Positional Value: ... 102 101 100 10-1 10-2 ...
Example:
743.15 = 7 * 102 + 4 * 101 + 3 * 100 + 1 * 10-1 + 5 * 10-2
Operating in a computer is done in a binary system.
Base (Radix): 2
Absolute Digit: 0.1
Positional Value: ... 22 21 20 2-1 2-2 ...
Example:
00110 = 0 * 24 + 0 * 23 + 1 * 22 + 1 * 21 + 0 * 20
Octal number system
Base (Radix): 8
Absolute Digit: 0,1,2 ... 7
Positional Value: ... 82 81 80 8-1 8-2 ...
Octal number system is based on 8 and has eight symbols
Different numbers 0,1,2 ... 7. In an octal number can be described in
exponent base 8.
System Hexadecimal Numbers
Base (Radix): 16
Absolute Digit: 0,1,2 ... 9, A, B, C, D, E, F
Positional Value: 162 161 160 16-1 ... 16-2 ...
Example:
Convert to decimal numbers 110 112
110112 = 24 + 23 + 21 + 20
= 16 + 8 + 2 + 1
= 2710
Convert 7568 to decimal numbers
7568 = 7 * 82 + 5 * 81 + 6 * 80
= 448 + 40 + 6
= 49 410
Convert to decimal number 31A16
31A16 = 3 * 162 + 1 * 161 + 10 * 160
= 768 + 16 + 10
= 79 410
Conversion from one number system to decimal number system
Convert to decimal numbers 110 112
110112 = 24 + 23 + 21 + 20
= 16 + 8 + 2 + 1
= 2710
Conversion to a binary number system octal number system
10110111.1011102
we will classify the three-three:
010 110 111, 101 1102 = 267.568
Conversion to the octal number system binary number system
Formula:
Return the octal value in accordance with the corresponding binary value
Example:
745.238 = 111 100 101, 010 0112
= 111,100,101.0100112
Converting the binary number system to hexadecimal number system
Formula:
• Group the four-four.
• If less than four given a 0 in front for the numbers in front of the comma and the
back to numbers after the decimal point.
Example:
1011110111.011010002
we will classify the four-four:
0010 1111 0111, 0110 10002 = 2F7, 6816
Converting hexadecimal number system into binary number system
Formula:
Return the hex value in accordance with the corresponding binary values (see table)
Example:
ABC, DE16 = 1010 1011 1100 1110 11 112
= 101,010,111,100.111011112
Table Converting hexadecimal numbers to binary
Hexadecimal Binary Hexadecimal Binary
0 0000 8 1000
1 0001 9 1001
2 0010 A 1010
3 0011 B 1011
4 0100 C 1100
5 0101 D 1101
6 0110 E 1110
7 0111 1111 F
