this is exactly correct

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this is exactly correct

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In simple English, binary means
‘two’. Hence binary numeral system is a way to represent numbers using only
two digits – 0 and 1. This system is widely used in computers to do all the
tasks like calculations, taking logical decisions etc. Each successive digit
represents a power of 2.

**Coversion from binary to decimal**:

1. Write down the binary number and list the powers of 2 from right to left.

2^6 2^5 2^4 2^3 2^2 2^1 2^0

1 0 1 1 0 0 1

2. Write the digits of the binary number below their corresponding powers of two.

64 32 16 8 4 2 1 (Power of two)

1 0 1 1 0 0 1 (binary number)

3. Multiply the digits in the binary number with their corresponding powers of two and add them.

(64*1) + (32*0) + (16*1) + (8*1) + (4*0) + (2*0) + (1*1) = 89

4. Write the answer along with its base subscript.

(89)base 10 = (1011001) base2

**Coversion from decimal to binary:**

1. Take the decimal number you want to convert.

(89)base10

2. Divide the number by 2 and keep track of the remainder.

89 / 2 = 49; Remainder = 1

3. If dividend is odd, remainder = 1 and if dividend = odd, remainder = 0.

4. Continue downwards, dividing each new quotient by two and writing the remainders to the right of each dividend. Stop when the quotient is 0.

89 / 2 = 44; Remainder = 1

44 / 2 = 22; Remainder = 0

22 / 2 = 11; Remainder = 0

11 / 2 = 5; Remainder = 1

5 / 2 = 2; Remainder = 1

2 / 2 = 1; Remainder = 0

1 / 2 = .5; Remainder = 1

5. Starting with the bottom remainder, read the sequence of remainders upwards to the top

(1011001) base2 = (89) base10

1. Write down the binary number and list the powers of 2 from right to left.

2^6 2^5 2^4 2^3 2^2 2^1 2^0

1 0 1 1 0 0 1

2. Write the digits of the binary number below their corresponding powers of two.

64 32 16 8 4 2 1 (Power of two)

1 0 1 1 0 0 1 (binary number)

3. Multiply the digits in the binary number with their corresponding powers of two and add them.

(64*1) + (32*0) + (16*1) + (8*1) + (4*0) + (2*0) + (1*1) = 89

4. Write the answer along with its base subscript.

(89)base 10 = (1011001) base2

1. Take the decimal number you want to convert.

(89)base10

2. Divide the number by 2 and keep track of the remainder.

89 / 2 = 49; Remainder = 1

3. If dividend is odd, remainder = 1 and if dividend = odd, remainder = 0.

4. Continue downwards, dividing each new quotient by two and writing the remainders to the right of each dividend. Stop when the quotient is 0.

89 / 2 = 44; Remainder = 1

44 / 2 = 22; Remainder = 0

22 / 2 = 11; Remainder = 0

11 / 2 = 5; Remainder = 1

5 / 2 = 2; Remainder = 1

2 / 2 = 1; Remainder = 0

1 / 2 = .5; Remainder = 1

5. Starting with the bottom remainder, read the sequence of remainders upwards to the top

(1011001) base2 = (89) base10