Convert decimal number 26.85 into binary equivalent.
11010.110110
To convert the decimal number 26.85 into its binary equivalent, follow these steps:
- Convert the integer part (26):
- Divide the integer part by 2 and record the remainder.
- Continue dividing the quotient by 2 until the quotient is zero.
- Write down the remainders in reverse order.
26 ÷ 2 = 13 remainder 0
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1Writing in reverse order gives: 11010
- Convert the fractional part (0.85):
- Multiply the fractional part by 2.
- Record the integer part of the result (0 or 1).
- Use the new fractional part for the next iteration.
- Repeat until the fractional part becomes zero or until the desired precision is achieved.
0.85 x 2 = 1.70 → Integer part = 1 (Fractional part = 0.70)
0.70 x 2 = 1.40 → Integer part = 1 (Fractional part = 0.40)
0.40 x 2 = 0.80 → Integer part = 0 (Fractional part = 0.80)
0.80 x 2 = 1.60 → Integer part = 1 (Fractional part = 0.60)
0.60 x 2 = 1.20 → Integer part = 1 (Fractional part = 0.20)
0.20 x 2 = 0.40 → Integer part = 0 (Fractional part = 0.40)The binary fractional part stops at (0.40)∞, giving 110110 with desired precision.
Therefore, the binary equivalent of the decimal number 26.85 is 11010.110110.
The correct answer is 11010.110110.
Important Questions from Binary Number System
- The decimal number equivalent to binary digit 110 is ______.
- If $(L)_M$ represents a number L in base-M number system, then identify the correct descending order of the following numbers A-D when converted to decimal number system.
A. $(20003.2)_4$
B. $(111111.11)_2$
C. $(732.2)_8$
D. $(C2.6)_{16}$
Choose the correct answer from the options given below : Given below are two statements with reference to different number systems:
Statement I: (D6C1)16 = (54977)10
Statement II: (41819)10 = (A35B)16
In the light of the above statements, choose the correct answer from the options given below:An Indian company designs a mobile application to process staff records. In each record, 10 bits are used to store staff ID and 20 bytes are used to store staff names. How many staff records can the mobile application support?
Match List I with List II
LIST I (Statement) List II (Value) A. Number of bytes formed from 8 bits I. 6 B. Base-10 (denary) value of the binary number : 110 II. 4 C. If there are 2ᴾ bytes in 1 mega byte, then what is the value of P ? III. 1 D. An ISP company advertises its broadband download speed as 128 mega bits per second. How many 4-mega byte files can be downloaded per second using the company's broad band? IV. 20 Choose the correct answer from the options given below:
