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# Questions tagged [binary]

For questions about representing numbers in base 2 or performing arithmetic on them.

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### How much time (in hours) will it take to check if the number with 20 binary digits is the prime number?

How much time (in hours) will it take to check if the number with 20 binary digits is the prime number, in problem it's mentioned that for number with 10 digits it took 1 hour it's also said that the ...
36 views

### Converting IPV4 address into Binary

So given an IP address it is converted into binary via calculating the binary of all different segments and then joining them. For example, 12.32.18.01 converted into a binary it would amount to this ...
29 views

### Convert scientific notation decimal number to binary

I'm given the number: $$8.881784197001252 \cdot 10^{-16}$$ I know it is $2^{-50}$ but suppose I didn't know. I need to convert it to binary. One way is to apply the school taught algorithm on the ...
49 views

### Minimum number of bits to represent negative number

Minimum number of bits required to represent $(+32)_{base10}$ and $(-32)_{base10}$ in signed two's compliment form? My attempt: 32 = 0100000 ( 1st zero - sign bit as positive) So to represent +32 ...
33 views

### Fundamental motivation behind the use of bits and binary representation

This is a naive question, but what makes binary representation special from a theoretical standpoint and from the standpoint of information theory? If for technical reasons building ternary computers ...
38 views

### How to convert 010111 to decimal using only odd numbered positions while still applying the correct positional exponent?

I am trying to understand what this question is asking in terms of conversion. I know how to convert binary to decimal and vice versa, but the method you need to use has me confused. I need to ...
22 views

### What's the least signifcant bit of a mantissa system?

If Mantissa is a 1-dot-M fixed-point number whose most significant bit is always 1 then, how is the least significant bit calculated? I know the least and most significant bit of the mantissa ...
227 views

### checking '<' for two binary numbers in a cnf-formula

I want to check whether a arbitrary binary number is less or equal to another binary number in a cnf-formula. I can already construct a formula, which is not in cnf: Lets say n and m are two-digit ...
38 views

### Binary to Decimal Algorithm Explanation

I came across some code today for converting binary to decimal, and I realised that I don't fully understand how it works. Here it is in Python: ...
22 views

### Why does going from 2's complement (in binary) to the positive value by completing to 1 then adding 1 work?

I'm studying Computer science and this has confused me for a long time since our professor didn't give any proof. When changing from 2's complement to the positive value, we can go in reverse (by ...
92 views

### Is decimal number 8 represented as 3 bits or 4 bits in computer?

I was told by my professor that "It takes c * ln(n) bits to store a number n, where ln() is base 2 and c is a constant." Thus, to store a number 8, we need ln(8) = 3 bits(I think const c can be ...
29 views

### Conversion from octal numerical system to binary numerical system

I know that in order to convert a numeral in base-8 to a numeral in base-2 I can write each octal digit as a binary word of 3 bits. I know that 2^3 = 8 that is exactly the dimension of the base of ...
50 views

### Can we represent $\sqrt{2}$ exactly even with infinite bits in mantissa [closed]

Can we represent $\sqrt{2}$ exactly even with infinite bits in mantissa in floating point notation or otherwise. We actually have to prove this is not possible. But why can't we if we have infinite ...
142 views

### Binary representation of 129 when using 8bits for two's complement?

I have this confusion regarding binary representation of decimal value 129 (or even 128). If 8 bits are used to represent numbers when doing the two's complement, then we know that '00000000' to '...
23 views

### For signed integers, why don't representative the smallest number as all zeros in binary, and the largest as all ones?

I'm reading up on bitwise operators, complements, and two's complements, and I'm wondering why the lower limit of a range (aka lowest negative number) isn't all zeroes in binary, and the upper limit ...