Name: Order of Operations on Expressions
Uploaded: 2019-07-19
Duration: 6 min 31 s
Description: If we want to solve an expression, we need to follow some basic procedure to solve it. Watch this video and learn more on how to solve expressions in a simpl...

Question

How are number represented in binary system? Represent

38, 95, 162

and

512

in binary system.

Accepted Answer

Each digit in a binary number is called a bit. The number $1010110$ is represented by $7$ bits. To see how many digits a number needs, you can simply take the logarithm (base $2$ ) of the number, and add $1$ to it. The integer part of the result is the number of digits.

Step $1$ : Divide the number by $2$ . Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes $0$ .

Step 2: Write the remainder from bottom to top i.e. in the reverse chronological order.

Dividend Remainder

$38 \div 2 = 19$ $0$

$19 \div 2 = 9$ $1$

$9 \div 2 = 4$ $1$

$4 \div 2 = 2$ $0$

$2 \div 2 = 1$ $0$

$1 \div 2 = 0$ $1$

Binary number for $38$ is $10010$

Dividend Remainder

$95 \div 2 = 47$ $1$

$47 \div 2 = 23$ $1$

$23 \div 2 = 11$ $1$

$11 \div 2 = 5$ $1$

$5 \div 2 = 2$ $1$

$2 \div 2 = 1$ $0$

$1 \div 2 = 0$ $1$

Binary number for $95$ is $1011111$

Dividend Remainder

$162 \div 2 = 81$ $0$

$81 \div 2 = 40$ $1$

$40 \div 2 = 20$ $0$

$20 \div 2 = 10$ $0$

$10 \div 2 = 5$ $0$

$5 \div 2 = 2$ $1$

$2 \div 2 = 1$ $0$

$1 \div 2 = 0$
$1$

Binary number for $162$ is $10100010$

Dividend Remainder

$512 \div 2 = 256$ $0$

$256 \div 2 = 128$ $0$

$128 \div 2 = 64$ $0$

$64 \div 2 = 32$ $0$

$32 \div 2 = 16$ $0$

$16 \div 2 = 8$ $0$

$8 \div 2 = 4$ $0$

$4 \div 2 = 2$ $0$

$2 \div 2 = 1$ $0$

$1 \div 2 = 0$ $1$

Binary system for $512$ is $1000000000$

How are number represented in binary system? Represent $38, 95, 162$ and $512$ in binary system.

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