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Binary numbers are a real challenge....
I need help understanding binary numbers for my computer class. We have a quiz this Thursday and he just introduced this today. In computer, I think it only uses 0 and 1 to compute any number. This is confusing me, so if anyone can help me, it is greatly appreciated. I know this is not an advice question but I need any help I can get!
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Binary is a way of counting by using only 1 and 0. This is useful in electronics because electric current can be either on(1) or off(0). It's not in itself a way of computing numbers.
Decimal, our normal system, only goes up to 9. After that, you have to add another number. 9+1=10. The ones place turns into a 0 and the tens place gets a 1.
Binary only goes up to 1. After that, you have to add another number. 1+1=10. The ones place turns into a 0 and then twos place gets a 1. In binary, 10 isn't said as "ten", it's said as "one-zero".
Counting:
-111+1=1000. The ones, twos, and fours places are full so we turn everything into a 0 and add a 1 in the the eights place.
-101+1=110. The ones place is full so we turn it into a 0 and add a 1 in the twos place.
-101111+1=110000. The ones, twos, fours, and eights places are full, so we turn them all into 0s and add a 1 in the sixteens place.
Look at a binary number such as 11111111111.
From right to left, the places are:
(1)ones
(2)twos
(3)fours
(4)eights
(5)sixteens
(6)32
(7)64
(8)128
(9)256
(10)512
(11)1024
From binary to decimal:
-1000=8. There is a 1 in the eights place.
-1100=12. There is a 1 in the eights place PLUS a 1 in the fours place. 8+4=12.
-101010=42. There is a 1 in the thirtytwos place PLUS a 1 in the eights place PLUS a 1 in the twos place. 32+8+2=42
From decimal to binary:
-20=10100. Start with a blank binary number: 0000000. Add the largest number possible with just 1 changed digit: 0010000=16. You now have 4 left, so add that to the number: 0010100. Cut off the leading zeros: 10100.
-54=110110. Start with a blank binary number:0000000. Add the largest number possible with just 1 changed digit: 0100000=32. You now have 22 left, so repeat. 0010000=16. Add it to the previous: 0110000=48. You now have 6 left, so repeat. 0000100=4. Add it to the previous: 0110100=52. You have 2 left, so add it to the number: 0110110=54. Cut off the leading zero: 110110
On the left is binary, on the right is decimal:
0 0
1 1
10 2
11 3
100 4
101 5
110 6
111 7
1000 8
1001 9
1010 10
1011 11
1100 12
1101 13
1110 14
1111 15
10000 16
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