Question

(1) Convert these decimal numbers into binary numbers.
(i)2589
(ii)258
(iii)1024
(iv) 256
(v) 968

(2) Convert these binary numbers into decimal numbers.
(i) 1001010
(ii) 10001010
(iii) 100000010
(iv) 0100001011
(v) 101010101010


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Answer 1

Answer:

1. 2589 = 101000011101
2. 258 = 100000010
3. 1024 = 10000000000
4. 256 = 100000000
5. 968 = 1111001000

1. 10010101 = 74
2. 10001010 = 138
3. 100000010 = 258
4. 0100001011 = 267
5. 101010101010 =2730

Explanation:

2| 2589 | ( always divide by 2)

2 | 129 4 |1

2 | 647 |0

2 | 323 |1

2 | 161 |1

2 | 80 |1

2 | 40 |0

2 | 20 |0

2 | 10 |0

2 | 5 |0

2 | 2 |1

2 | 1 |0

2 | 0 |1 ⬆️( move in this direction)

Write the Remainders from bottom to top

2589 = 101000011101

Binary to decimal

ex: 1001= binary

decimal conversion =

(binary digit number) *2^(no.of binary digits -1)

no.of binary digits (1001) = (4-1) =3

1001 = (1 * 2^3) + (0*2^2) +(0*2^1)+(1*2^0)

1001= (1*8)+(0)+(0)+(1)

1001 =(9)

or

simply start from units place multiply with

${2}^{0}$

in go on increase 1 power

$1001010 = (1 \times 2 {}^{6} ) + (0 \times {2}^{5} ) + (0 \times 2 {}^{4} ) + (1 \times 2 {}^{3} ) + (0 \times 2 {}^{2} ) + (1 \times 2 {}^{1} ) + (0 \times 2 {}^{0} )$

$\\ 1001010 = 64 + 0 + 0 + 8 + 0 + 2 + 0$

$\\ 1001010 = 74$

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