this is exactly correct

Log in to add a comment

this is exactly correct

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

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