Binary is a number system with only two digits. Each position is a power of two, and a number is the sum of the powers that are switched on.
About 2 min of reading
Count and read binary rows.
Print the first eight numbers in binary.
Before you run it, say out loud what it will print. Then open the answer.
Read a row as a number.
Before you run it, say out loud what it will print. Then open the answer.
Show all four ones.
Before you run it, say out loud what it will print. Then open the answer.
Check that ten is eight plus two.
Before you run it, say out loud what it will print. Then open the answer.
Read the first example one line at a time. A line that prints shows what appears on screen; the rest set things up quietly.
A machine only has two states, so base two needs no translation. Decimal would have to be built out of bits, which is what binary already is.
Adding in binary carries when a column gets two, exactly as decimal carries at ten. The mechanics you know already apply.
print(0b1000)
print(0b100)
print(0b10)A single 1 followed by zeros is a power of two: 8, 4, 2. Binary is those powers added together.
print(0b1010)That row has the 8 and the 2 switched on, so it reads as ten. Every position is worth double the one on its right.
print(0b1111)Four ones is 8 plus 4 plus 2 plus 1, which is fifteen. All ones is always one less than the next power.
for i in range(8):
print(bin(i))Counting up adds one to the row, and the carry rolls left the same way decimal carries.
print(int("10110", 2))Text read as base two gives twenty two. The digits are weights, not counts of things.
print(0b1, 0b10, 0b100, 0b1000)Moving a 1 one place left doubles it. That doubling is the whole rule of the system.
print(0b10 == 2)There is no digit three in binary, so two is written as one followed by zero. The count of digits grows fast.
print(12, bin(12))The same number written in decimal and in binary. The value is one thing, the writing is a choice.
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