pls help me to solve this question.
thank you very much
binary-decimal conversion
a.101=
b.1100=
c.100110=
d.111111=
decimal binary conversion
a.1216
10
b.2121
10
just like a number like
34610 = 3(10^2) + 4(10^1) + 6(10^0)
a binary number like
c) 1001102 = 1(2^5) + 0(2^4) + 0(2^3) + 1(2^2) + 1(2^1) + 0(2^0)
= 32 + 0 + 0 + 4 + 2 + 0 = 38
do the others the same way
to do the reverse you will have to know the powers of 2
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
etc.
so to change 1216(base10) to base 2
the largest power of 2 that divides into it is 1024
so
1216 = 1024 + 128 + 64
=1(2^10) + 0(2^9) + 0(2^8) + 1(2^7) + 1(2^6) + 0(2^5) + 0(2^4) + 0(2^3) + 0(2^2) + 0(2^1) + 0(2^0)
= 100110000002
do the other one the same way
Sure, I'd be happy to help you solve these questions on binary-decimal conversion.
For the first set of questions, where you need to convert binary numbers into decimal numbers:
a. 101 = ?
To convert a binary number to a decimal number, you need to start from the rightmost digit of the binary number (the least significant bit) and multiply each digit by powers of 2, increasing from right to left. So, for 101:
1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 4 + 0 + 1 = 5
Therefore, 101 in binary is equal to 5 in decimal.
b. 1100 = ?
Using the same process:
1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 0 * 2^0 = 8 + 4 + 0 + 0 = 12
Therefore, 1100 in binary is equal to 12 in decimal.
c. 100110 = ?
1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0 = 32 + 0 + 0 + 4 + 2 + 0 = 38
Therefore, 100110 in binary is equal to 38 in decimal.
d. 111111 = ?
1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 32 + 16 + 8 + 4 + 2 + 1 = 63
Therefore, 111111 in binary is equal to 63 in decimal.
Now let's move on to the second set of questions, where you need to convert decimal numbers into binary numbers:
a. 1216 = ?
To convert a decimal number to a binary number, you need to repeatedly divide the decimal number by 2 and note the remainder until the quotient becomes 0. Then, write the remainders in reverse order to get the binary equivalent.
Let's apply this approach to 1216:
1216 divided by 2 is 608 with a remainder of 0
608 divided by 2 is 304 with a remainder of 0
304 divided by 2 is 152 with a remainder of 0
152 divided by 2 is 76 with a remainder of 0
76 divided by 2 is 38 with a remainder of 0
38 divided by 2 is 19 with a remainder of 1
19 divided by 2 is 9 with a remainder of 1
9 divided by 2 is 4 with a remainder of 1
4 divided by 2 is 2 with a remainder of 0
2 divided by 2 is 1 with a remainder of 0
1 divided by 2 is 0 with a remainder of 1
So, reading the remainders from bottom to top, the binary equivalent of 1216 is 10011000000.
b. 2121 = ?
Applying the same process:
2121 divided by 2 is 1060 with a remainder of 1
1060 divided by 2 is 530 with a remainder of 0
530 divided by 2 is 265 with a remainder of 0
265 divided by 2 is 132 with a remainder of 1
132 divided by 2 is 66 with a remainder of 0
66 divided by 2 is 33 with a remainder of 0
33 divided by 2 is 16 with a remainder of 1
16 divided by 2 is 8 with a remainder of 0
8 divided by 2 is 4 with a remainder of 0
4 divided by 2 is 2 with a remainder of 0
2 divided by 2 is 1 with a remainder of 0
1 divided by 2 is 0 with a remainder of 1
So, the binary equivalent of 2121 is 100001001001.
I hope this helps! Let me know if you have any further questions.