Page 40 - Cs_withBlue_J_C11_Flipbook
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b. position of the digits
c. the base of the number system
This logical representation of numbers is the basis of all mathematical and algebraic calculations.
2. Write the steps to convert a decimal number into a binary number.
Ans. The steps to convert a decimal number into a binary number are as follows:
1. Divide the number by 2 and store the remainder of the division separately.
2. Assign quotient as the new dividend.
3. Repeat steps 1 and 2 until new dividend = 0.
4. Arrange the remainders from bottom (LSB) to top (MSB) to get the result.
5. For real numbers, the above process is to be followed for the integer part.
6. Now, for the decimal part, the steps are as follows:
a. Multiply fractional part by 2 and store the integer part of the product separately.
b. Repeat above step until the fractional part becomes 0 or up to 4 places of decimal.
c. Arrange the binary digits of the integer part from top to bottom for the result of the fractional part.
3. Convert (0.425) to:
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a. Binary b. Octal c. Hexadecimal
Ans. a. Fractional part
Multiplication Result Integer part
0.425 × 2 = 0.850 0
0.850 × 2 = 1.700 1
0.700 × 2 = 1.400 1
0.400 × 2 = 0.800 0
(0.425) = (0.0110) 2
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b.
Fractional part
Multiplication Result Integer part
0.425 × 8 = 3.4 3
0.4 × 8 = 3.2 3
0.2 × 8 = 1.6 1
0.6 × 8 = 4.8 4
(0.425) = (0.3314) 8
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c. Fractional part
Multiplication Result Integer part
0.425 × 16 = 6.8 6
0.8 × 16 = 12.8 12(C)
0.8 × 16 = 12.8 12(C)
0.8 × 16 = 12.8 12(C)
(0.425) = (0.6CCC) 16
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4. Convert (10111011.1011) to decimal.
2
Ans. 7 6 5 4 3 2 1 0 -1 -2 -3 -4
1 0 1 1 1 0 1 1 . 1 0 1 1
2
3
4
1
-2
-3
0
-1
6
7
5
= 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 -4
= 128 + 32 + 16 + 8 + 2 + 1 + 1/2 + 1/8 + 1/16
= (187.6875)
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3838 Touchpad Computer Science-XI

