Do as directed:
(a) Convert the Decimal number 781 to its Binary equivalent.
(b) Convert Binary number 101101.001 to its decimal equivalent
(c) Convert Octal number 321.7 info its Binary equivalent
Answer:
(a) 781 _{ 10 } to its binary equivalent
Therefore, 781 _{ 10 } = 1100001101 _{ 2 }
Explanation:
- Repeatedly divide the decimal number by 2 until the quotient becomes 1 and record all the remainders.
- The remainders should be written bottom to upwards to get the binary equivalent of the decimal number.
(b) 101101.001 _{ 2 } to its decimal equivalent
101101.001 = 1 x 2 ^{ 5 } + 0 x 2 ^{ 4 } + 1 x 2 ^{ 3 } + 1 x 2 ^{ 2 } + 0 x 2 ^{ 1 } + 1 x 2 ^{ 0 } + 0 x 2 ^{ -1 } + 0 x 2 ^{ -2 } + 1 x 2 ^{ -3 }
= 32 + 0 + 8 + 4 + 0 + 1 + 0 + 0 + 0.125
= 45.125 _{ 10 }
Explanation:
- To obtain the decimal equivalent of a binary number, individual digits of binary number should be multiplied by powers of 2 starting with the rightmost digit multiplied by 2 ^{ 0 } , second last digit multiplied by 2 ^{ 1 } , third last digit multiplied by 2 2 and so on up to the leftmost digit.
- For digits after the decimal point, the leftmost digit should be multiplied by 2 ^{ -1 } and the next digit by 2 ^{ -2 } and so on up to the rightmost digit.
(c) 321.7 _{ 8 } to its binary equivalent
3 |
2 |
1 |
7 |
011 |
010 |
001 |
111 |
Therefore, 321.7 _{ 8 } = 11010001.111 _{ 2 }
Explanation:
- To obtain binary equivalent of an octal number, individual digits of octal number should be converted to binary in groups of three digits as given in the table below.