Give in hexadecimal, the sum of these two hexadecimal numbers: 1A + 1B =?

Question

please explain

Answer 1

In decimal system - 35

In hexadecimal - 23

Answer 2

35 (in hex)

In binary, the place values from right to left are

etc<-- 2^8(256) ; 2^7(128); 2^6(64); 2^5(32); 2^4(16); 2^3(8); 2^2(4); 2^1(2), and 2^0(1)

So, 11100101(binary) = 128+64+32(skip the next two places, 16 and 8) + 4 (skip the next place, 2) + 1 = 229 (decimal).

In our regular decimal notation, the place values are
etc <- 10^5(100000); 10^4(10000); 10^3(1000); 10^2(100); 10^1(10); 10^0(1).

So, 5678 (decimal) = (5x10^3) + (6x10^2) + (7x10^1) + (8x10^0)

Now, in hex, the place values are
etc <-- 16^4 (65536); 16^3 (4096); 16^2 (256); 16^1 (16); 16^0 (1)

Whatever the base is, so many digits are used, e.g. base 2 , 2 digits (0 and 1); base 8 , 8 digits (0 to 7),; base 10, 10 digits (0 to 9). and base 16? Obviously, 16 digits. But THAT IS THE PROBLEM. We only have 10 digits. So, 10=A, 11=B ...15=F.

In your example, 1A = (1x16^1) + (10x16^0) = 16+10 = 26(decimal) and 1B = (1x16^1) + (11x16^0) = 16 + 11 = 27 (decimal).
If you add 26 and 27, you get 53 (all decimal). Since it is hex, divide by 16, you get 3 remainder 5. That five is your first digit on the RIGHT in hex. Since 3 is less than 16, you don't have enough to divide it for the third place, so the 3 fits in the second place, giving you 35(hex).

A somewhat different and easier method:

Set the two numbers down on paper like a normal addition, with A directly above B. If A=10 and B=11, you get 21. How many 16s can you find in that? Obviously only one (which will carry over to the next colunm on the LEFT). Put the remainder under the column with A and B. That will be 5. In the other column, you add 1 to 1 plus the other one you carried forward, you get 3. Put that down under the ones. Done!!!

Of course, if the numbers had been different in the second column (on the left) so that on adding them and the carried forward (if any) number, you get more than 16, you would divide by sixteen and carry forward that to the third column, while you put the remainder under the second column.

Oh, well, use your scientific calculator. Remember to set it to hex.

Hope this helps.

Answer 3

Instead of doing what everyone else did and give you the answer, i will show you how to do it.
both binary and hex counting systems work exactly the same, only you dont have as many digits

with a 10 digit based system you count up to 9 (0 is a digit)

0
1
2
3
4
5
6
7
8
9

when you get to 9, there is no more digits. so we change it back
to 0 and ad another place

10
11
12
13
14
15
16
17
18
19

and another place

20
21
22

eventually we get to

99

both places are at maximum, so we add another place.(both 9's to 0 and ad 1 to next place)

100


This is how the binary system works. EXACTLY the same, only with 2 digits. 0 and 1

start with

0 (0)

then go up

1 (1)

now we are at the highest digit, in binary 1, in decimal its 9. so, set the digit back to 0 and add a place

10 (2)

so we start with the right place and start counting up. in decimal 0-9, in binary 0-1

11 (3)

now we have both places are at the top digit (1). so reset both to 0 and add a place

100 (4)
101 (5)
110 (6)
111 (7)
1000 (8)
1001 (9)
1010 (10)
1011 (11)
1100 (12)
1101 (13)
1110 (14)
1111 (15)

Hex is exactly the same, just more digits 0-f

0
1
2
3
4
5
6
7
8
9
a (10)
b
c
d
e
f (15)

next digit

10 (16)
11
12
13
14
15
16
17
18
19
1a
1b
1c
1d
1e
1f (31)

another digit

100 (32)
101
102
103
104
105
106
107
108
109
10a (42)
10b
10c
10d
10e
10f (43)

another place

110 (44)
111
112
113
114
115
116
117
118
119 (53)
11a (54)
11b
11c
11d
11e
11f (59)

another place

120 (60)
121
122
123
124
125
126
127
128
129 (69)
12a (70)
12b
12c
12d
12e
12f (75)

next place goes up

130



oh, in windows calculator, hit view then scientific. you can then chose several different numbering systems.

:)

Answer 4

1A + 1B = (35)Hex
To verify the result, I convert 1A, 1B & 35 in decimal and found correct.
(1A)hex = (26)dec
(1B)hex = (27)dec
(35)hex = (53)dec.

addition, substraction of any two number with any base is very easy, just add the number starting from left each digit at one time, and if the result of operation of any of two digit exceed or equal to the maximum number possible in that number system ( 16 incase of hex) just carry one and keep counting the extra number (for example A + B = (15)hex, as A = 10 & B = 11 so A + B = 21, now 21 is 5 more than 16, so first digit is 5 and 1 goes as carry, which we put in front of 5.
you can verify the result (15)hex = (1*16 + 5) = 21.

so if you got the method, then please answer following two questions.
1. [(125) for base 6] + [(254) for base 6]
2. [(254) for base 6] - [(125) for base 6]

Thanks,
Anuj Kumar

Answer 5

1A+1B=35
explanation : A=10, B=11, A+B=21
21/16=1 with reminder 5

carry=1

so 1+1+1=3 and reminder 5

the answer is 35.

Answer 6

1A and 1B are hexidecimal numbers.

You are used to decimal, a system whose ten digits are 0 to 9 and when you get to the maximum digit plus one (9 + 1), you carry a 1 to the next digit and set the first digit to 0 (i.e. 10).

In hexidecimal, the sixteen digit system uses 0 to F (that is, 0 - 9, A, B, C, D, E and F). Similar to decimal, when you get to the maximum digit plus one (F + 1), you carry a 1 to the next digit and set the first digit to 0 (i.e. 10). "10" in hexidecimal is "16" in decimal.

So they are asking you to add 1A + 1B. That is equivalent to (10 + A) + (10 + B) in hexidecimal...which is (16 + 10) + (16 + 11) in decimal.

Now it is a simple matter of adding these values together and representing the result in hexidecimal.

Good luck!

Answer 7

35

Answer 8

35 in hex
53 in dec

1A in hex = 26 in dec
1B in hex = 27 in dec
26+27 =53 ( i hope you ca calculate in the decimal system )
and 53 in dec = 35 in hex

alternatively use windows calculator(scientific version)

Answer 9

35

I used calc

1A + 1B = 35