Question: Binary & Hexadecimal

[Amathproblem22]

I don't need help with a problem just help with easy ways of tackling the problems. Below are my current methods. (Hopefully, all is correct I was in a rush).

Binary to Decimal:

128	64	32	16	8	4	2	1
1	1	1	1	0	0	0	1

I already know \(\displaystyle 128+64+32= 224\) so then \(\displaystyle 16+1=17\), meaning \(\displaystyle 224+17=241\)

Decimal to Binary:
\(\displaystyle 79\)

128	64	32	16	8	4	2	1
0	1	0	0	1	1	1	1

So I do this by basically figuring what adds up to 79 or by figuring if the number can fit into any (hopefully that makes sense).

Binary to Hexadecimal:

8	4	2	1	8	4	2	1
1	0	1	0	0	1	0	1

I break it up into two sets of 8-4-2-1 and add up the 1's below it accordingly. \(\displaystyle 10=A\) in the first column, and \(\displaystyle 5\) in the scond column so \(\displaystyle A5\)

Hexadecimal to Binary:
\(\displaystyle B4\)
\(\displaystyle B=11,4=4\) so I but ones in the columns above so it adds up to the desired numbers leaving me 10110100.

Hexadecimal to Decimal
Using B4 from above = 11, then times that by 16 which in this case is easy and = 176 then adding 4 = 180

 

[HOI]

The simplest way to change decimal to binary repeated division by 2. 79/2= 39 with remainder 1. 39/2= 19 with remainder 1. 19/2= 9 with remainder 1. 9/2= 4 with remainder 1. 4/2= 2 with remainder 0, 2/2= 1 with remainder 0 1/2= 0 with remainder . So 79= 100111. Notice that "1"s and "0"s are the reverse of those calculations.

Binary to hexadecimal is easy because 16= 2^4 = 10000 in binary. Divide the binary number into groups of 4 digits: 10100101= 1010 0101. Yes, 1010 is 8+2= 10 which is represented by "A" in hexadecimal and 0101 is 4+ 2= 6. 10100101 in binary is A6 in hexadecimal.

To go from hexadecimal to binary is also easy- convert each hexadecimal "digit" to binary.

B= 8+ 3= 1011 and 4 is 0100 so B4 is 10110100.
For something more complicated, E423BF: E= 8+ 4+ 2= 1110. 4= 0100, 2= 0010, 3= 0011, B= 1011, and F is 1111 so E423BF is 111001000010001110111111 in base 2.

 

[Amathproblem22]

The simplest way to change decimal to binary repeated division by 2. 79/2= 39 with remainder 1. 39/2= 19 with remainder 1. 19/2= 9 with remainder 1. 9/2= 4 with remainder 1. 4/2= 2 with remainder 0, 2/2= 1 with remainder 0 1/2= 0 with remainder . So 79= 100111. Notice that "1"s and "0"s are the reverse of those calculations.

Binary to hexadecimal is easy because 16= 2^4 = 10000 in binary. Divide the binary number into groups of 4 digits: 10100101= 1010 0101. Yes, 1010 is 8+2= 10 which is represented by "A" in hexadecimal and 0101 is 4+ 2= 6. 10100101 in binary is A6 in hexadecimal.

To go from hexadecimal to binary is also easy- convert each hexadecimal "digit" to binary.

B= 8+ 3= 1011 and 4 is 0100 so B4 is 10110100.
For something more complicated, E423BF: E= 8+ 4+ 2= 1110. 4= 0100, 2= 0010, 3= 0011, B= 1011, and F is 1111 so E423BF is 111001000010001110111111 in base 2.

This is an easier version of what you were saying I guess halving by two and put a 1 if the number above is odd and a 0 if the number is 0.

0	1	2	4	9	19	39	79
0	1	0	0	1	1	1	1

Assuming you added A6 wrong? and dropped a 1 off 100111? Or was I wrong lol

 

[HOI]

Except that I would never say "halving by 2" (what else can you halve by?) that is essentially what I said.