Binary as data representation

Computer Science · Data representation

Flip the bits, change the value

Eight bits make a byte. Each switch is one bit. Flip it and watch the value: only the columns holding a 1 are added up.

Computer Science · Data and information

Data or information?

Sort each item. Is it raw data, or has it been given context so it means something?

6 of 6 still to sort.

Pick an item, then pick where it belongs. Ask yourself one thing: does anything tell you what it means?

Computer Science · How many sequences?

Why more values need more bits

Choose a 0 or a 1 for each bit and follow the branch to its end.

First bit → Second bit → Third bit

On Start. 2 branches to choose from.

Each bit is a 0-or-1 choice. Walk down a branch to build one sequence. A fourth bit would split every end into two more: 8 ends become 16.

What you need to know

• Data is raw facts and figures with no context; information is data given context, so it has meaning.
• Order matters in a sequence of symbols: 42 and 24 use the same digits but mean different things.
• Have a goPriya says 1.23 and 12.3 are "basically the same" because they use the same symbols. Is she right?

  No. Same symbols in a different order can mean something different.

  The order of the symbols carries meaning, so rearranging them can change what the sequence stands for.

• Binary uses just two symbols, 0 and 1, called bits. Bits combine to make binary sequences.
• In binary, place values double as you move left (1, 2, 4, 8, ...). Add up the ones that hold a 1.
• Check it: 10 is 2, 111 is 7 and 1110 is 14.
• Computers use a set number of bits, commonly 8 (a byte). Padding 0s at the front add nothing, so 14 is 00001110.
• Have a goDev writes 101 as 00000101 and says it is now a bigger number because it has more digits. What would you tell him?

  It is still the same number. The 0s at the front add nothing.

  Padding 0s fill the set number of bits but sit in columns that add nothing, so the value does not change.

• Any data and instructions can be held as binary sequences, as long as it is agreed what each sequence represents.
• The number of bits limits the different sequences: 3 bits give 8, 4 bits give 16, so more values need more bits.
• Have a goYou need a different sequence for each of 10 things. Are 3 bits enough? What about 4?

  3 bits are not enough (only 8). 4 bits are (16).

  Counting the things is not the test: the number of bits limits how many different sequences exist.

The big picture

Binary uses just two symbols, 0 and 1. Bits combine into sequences of a set length that can represent any data or instructions, once it is agreed what each sequence means. A binary number is the sum of the place values holding a 1, and the number of bits limits how many different things a sequence can identify.

⚠ Watch out

Counting the 1s instead of adding their place values, or thinking 0s padded on the front make a number bigger. Neither changes how the columns are added.

Memory hook

Bits do not carry meaning. The agreement does. And place values double as you go left.

Check yourself

Cover the page. Without looking, explain in two sentences why 1011 and 1101 are different numbers even though they use the same bits, and work out both values.