Binary equivalent of decimal number 35 is
100011
Two methods lead to the answer, and it is worth seeing both since one is faster and the other is more mechanical.
The first is to express 35 as a sum of powers of two. The powers available are 1, 2, 4, 8, 16, 32 and 64. Since 64 exceeds 35, start at 32: taking 32 leaves 3, and 3 is 2 plus 1. So 35 equals 32 plus 2 plus 1. Writing the six place values from 32 down to 1 and marking which are used gives 32 present, 16 absent, 8 absent, 4 absent, 2 present, 1 present - that is 1, 0, 0, 0, 1, 1, or 100011.
The second method is repeated division by 2, recording the remainders. Dividing 35 by 2 gives 17 remainder 1; 17 by 2 gives 8 remainder 1; 8 by 2 gives 4 remainder 0; 4 by 2 gives 2 remainder 0; 2 by 2 gives 1 remainder 0; and 1 by 2 gives 0 remainder 1. Reading the remainders from the bottom upwards gives 100011, confirming the first result. Reading them downwards instead is the classic error and would give 110001, which is the second option.
Checking the other distractors by converting back is quick. The value 110001 is 32 plus 16 plus 1, which is 49. The value 110101 is 32 plus 16 plus 4 plus 1, which is 53. The value 101011 is 32 plus 8 plus 2 plus 1, which is 43. None equals 35.
Converting the candidate answer back to decimal is always worth the few seconds it takes, since it catches both a misread place value and a reversed remainder sequence.
Hence the binary equivalent of 35 is 100011.
Similar Questions
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:
Match List I with List II
LIST I (Statement) LIST II (Value) A. Base-10 (denary) value of the binary number: 100000 I. 100 B. Internet service provider advertises a download speed of 80 megabits per second. What is the time taken in seconds to download an 80 megabyte file ? II. 14 C. A music file is 80 megabytes in size and MP3 file compression reduces the size of a music file by 90%. The number of MP3 files of the size after compression that can be stored on an 800 MB CD III. 32 D. What is the denary (base-10) equivalent to the hexadecimal digit E? IV. 8 Choose the correct answer from the options given below:
In the context of data stored in a computer, what is a byte?
Which of the following statements is/are correct?
(a) For the sequence of integers represented in binary as 00111, 01001, 01011, P………. the next integer P would be represented as 01101
(b) A byte is a binary number consisting of exactly 8 bits
Choose the correct option:
What is the decimal equivalent of binary number 1100110?
What is the binary equivalent of decimal number 75?
If the binary equivalent of the decimal number 53 is 110101, then the binary equivalent of the decimal number 50 is given by:
Symbols A-F are used in which one of the following?
Important Questions from Binary Number System
Convert decimal number 26.85 into binary equivalent.
- 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?
