Zeros and Ones

Think of the light switch in your room. It can be in only two states: on or off. There is nothing in between. During load-shedding, the power in a house was either there or not there. A cricket toss lands heads or tails. A question in a quiz can be answered yes or no.

A computer is built from switches like that, but tiny ones. They are called transistors, and they are switched by electricity, not by a finger. The chip inside a phone has billions of them, each one smaller than a germ. Each transistor is either on or off at any moment, and it can switch billions of times every second.

We write the two states as two digits:

• 1 for on,
• 0 for off.

A single 0 or 1 is called a bit, short for binary digit. “Binary” means “made of two”, like a bicycle’s two wheels. A bit is the smallest piece of information a computer can hold: it answers one yes-or-no question.

Everything a computer stores is kept as bits, though different devices keep them in different ways:

One bit can answer only one yes-or-no question. That is not much. But put bits side by side and they can make patterns, and each pattern can stand for something different.

With one bit there are 2 patterns: 0 and 1. With two bits there are 4: 00, 01, 10 and 11. How many with three?

Three bits make 8 patterns. Look at why: take the 4 patterns of two bits, and put a 0 in front of each, then a 1 in front of each. That is 4 + 4 = 8. Every bit you add doubles the number of patterns:

A group of 8 bits is called a byte. A byte has 256 different patterns, from 00000000 to 11111111. That is enough to give every capital letter, small letter, digit and punctuation mark of English a pattern of its own, with plenty to spare. So one byte can hold one letter of English text. (Nepali letters usually take more than one byte. You will find out why in Grade 7.)

You already know one way of writing numbers. It uses ten digits, 0 to 9, so it is called the decimal system (“deci” means ten). After 9, we have run out of digits, so we write 10: a 1 in the tens place and a 0 in the ones place. Each place is worth ten times the place to its right:

So 2083 means 2 thousands + 0 hundreds + 8 tens + 3 ones. Each digit is worth a different amount depending on its place.

A computer has only two digits, 0 and 1. So it counts in the binary system, also called base 2. It runs out of digits after 1, not after 9. So in binary, each place is worth two times the place to its right:

These numbers are the place values of binary. Each place holds a 0 (that place adds nothing) or a 1 (that place adds its value).

Counting goes like this. 0, then 1. Now the ones place is full. To add one more, the ones place goes back to 0 and we carry 1 into the next place, the twos: 10. That is two. Then 11 is three. Then both places are full, so both go back to 0 and the carry goes into the fours place: 100 is four. It is exactly what happens in decimal when 9 becomes 10, or 99 becomes 100, only much sooner.

Here are the numbers from 0 to 10 in binary:

Reading a binary number

To find what number a binary number stands for, write the place values over its digits, starting from 1 on the right. Then add the place values that have a 1 under them.

Writing a number in binary

To go the other way, from an ordinary number to binary, take the place values from the biggest one that fits.

1. Find the biggest place value that is not more than your number. Put a 1 there.
2. Take that place value away from your number.
3. Go to the next place to the right. If it fits into what is left, put a 1 there and take it away; if not, put a 0.
4. Carry on until you have done the ones place. What is left must be 0.

Look very closely at a phone’s screen, through a drop of water or a magnifying glass. The picture is made of tiny dots of light, in rows and columns. Each tiny dot is called a pixel, short for “picture element”. The moving red-dot signs in shops and on some buses work the same way, with dots you can see from across the road. So does a cross-stitch pattern on cloth.

The simplest kind of picture is black and white: every pixel is either black or white. That is just two states, so each pixel needs exactly one bit. We agree on a rule: 1 means black, 0 means white. Then a computer can keep a whole picture as rows of 0s and 1s: one row of bits for each row of pixels.

This is all a computer keeps of the picture: 64 bits, which is 64 ÷ 8 = 8 bytes. To show it, the computer reads the bits back, row by row, and lights each pixel the way its bit says. Anyone who knows the rule (1 = black, how many pixels a row) can turn the bits back into the picture.

More pixels, sharper pictures

An 8 × 8 picture looks blocky. Curved lines come out as steps, and small details vanish. Use more pixels, each one smaller, and the picture looks more like the real shape. The number of pixels across and down a picture is called its resolution. A picture of 32 × 32 pixels has a higher resolution than one of 8 × 8.

So there is a trade: a higher resolution gives a sharper picture, but it needs more bits to store and more time to send.

Photos in color need more than one bit for each pixel, because each pixel must say which of millions of colors it is. You will learn how in Grade 7. But the idea is the same: a photo is a grid of pixels, and each pixel is stored as bits.

You have heard sizes like “a 1 GB data pack”, “this video is 25 MB”, “the phone has 128 GB”. These are all ways of counting bytes.

A byte is small: one letter. So for bigger things we use bigger units. Computers count in powers of 2, so each unit is 1,024 times the one before (1,024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2, a round number in binary). For working things out in your head, “about a thousand” is close enough.