To convert the decimal number to binary number, repeated division by two is needed.
Examples: Convert following into binary numbers:
2 | 45 | 1 |
2 | 22 | 0 |
2 | 11 | 1 |
2 | 5 | 1 |
2 | 2 | 0 |
1 |
=(101101)_{2}
2 | 225 | 1 |
2 | 112 | 0 |
2 | 56 | 0 |
2 | 23 | 1 |
2 | 11 | 1 |
2 | 5 | 1 |
2 | 2 | 0 |
1 |
= (10111001)_{2}
To convert binary to the decimal number system, multiply given number by 2.
1. (1101)_{2}=(?)_{10}
=1x2^{3}+ 1 x 2^{2}+ 0x 2^{1}+ 1x 2^{0}=8 + 4 + 0 + 1
=13
A | B | A+B |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 with carry 1 |
1 | Carry | |||
1 | 1 | 0 | 0 | |
1 | 1 | 1 | 1 | |
11 | 0 | 1 | 1 |
A | B | A*B |
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
Binary numbers are added to the same manner as decimal numbers. There are only four possible combinations resulting from the addition of two binary digits.
Rules for binary addition:
A | B | A+B |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 10 |
i.e. 0 carry 1
The rules for subtraction are the same in the binary system as in the decimal system. The result of the subtraction of binary digit is either 0 or 1.
Rules for binary subtraction:
A | B | A-B |
0 | 0 | 0 |
1 | 0 | 1 |
1 | 1 | 0 |
0 | 1 | 1 |
Binary numbers are multiplied in the same manner as decimal numbers. We need to remember the rules of binary addition.
Rules for binary multiplication:
A | B | A×B |
0 | 0 | 0 |
1 | 0 | 0 |
0 | 1 | 0 |
1 | 1 | 1 |
=1x2^{3}+ 1 x 2^{2}+ 1x 2^{1}+ 0x 2^{0}=8 + 4 + 2 + 0
=14
2 | 45 | 1 |
2 | 22 | 0 |
2 | 11 | 1 |
2 | 5 | 1 |
2 | 2 | 0 |
1 |
=(101101)_{2}
According to binary addition, 1 + 1 equals to :
11
0 with carry 1
2
1
According to binary number system, 11 equals to :
1100 + 1111 equals to ________
To convert binary to decimal number system, multiply given number by ______.
2
10
8
16
To convert decimal number to binary number,repeated division by _____ is needed.
None of the answers are correct
2
1
10
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Rules of binary subtraction
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