ACARA Digital Technologies Years 7–8 — Binary Number Representation Hangman

The 21 key terms

1two-state system

A system with only two possible conditions, like a light switch being off or on. We write the two states as 0 and 1, which is the idea behind binary.

20 = off, 1 = on

A switch has two states. We write 0 for off and 1 for on, so a row of switches or LEDs can be written as binary digits, like 1 0 1 1.

3bit

A bit is a single binary digit that is either 0 or 1, like a switch that is off (0) or on (1). A group of 8 bits is called a byte.

4whole number

A number with no fraction or decimal part, like 0, 7 or 250. We use whole numbers to count things, such as scores, lives or students. 3.5 is not a whole number.

5decimal base-10, binary base-2

Decimal is base-10 and uses ten digits, 0 to 9. Binary is base-2 and uses only 0 and 1. People use decimal every day, but computers use binary.

6denary place value

Each denary column is worth 10 times the column to its right (1, 10, 100, 1000). A number is the sum of each digit times its column value, e.g. 345 = 300 + 40 + 5.

112^n - 1 >= number

Find the smallest number of bits n whose largest value, 2^n - 1, is at least your number. Example: 20 is too big for 4 bits (max 15), so it needs 5 bits (max 31).

12powers of 2

Binary place values: 1, 2, 4, 8, 16, 32, 64, 128 and so on. Each place is double the one before it, which is why binary is called base 2.

13most significant bit

The leftmost bit of a binary number. It has the biggest place value, so it changes the number the most. The rightmost bit is the least significant bit.

15Add the place values that have a 1

To read a binary number, add up the place values (1, 2, 4, 8...) that have a 1 under them and ignore the 0s. For example, 1011 is 8 + 2 + 1 = 11.

20nibble

A nibble is a group of 4 bits, so half a byte. Two nibbles make 1 byte. One hexadecimal digit fits exactly in one nibble.

21repeated division by 2

Divide a number by 2 again and again until the quotient is 0, noting each remainder. Read the remainders from last to first to get the binary number. Example: 13 is 1101.

22convert back

Check a decimal to binary answer by reading the binary back into decimal, adding the place values, and comparing with the starting number. If they match, it is right.

23binary conversion mistake

A slip such as reversing place values, dropping a zero, reading remainders top to bottom or using a 2. Binary only uses 0 and 1, and remainders are read bottom to top.

24=DEC2BIN(13)

A spreadsheet function that converts a decimal whole number into binary text. =DEC2BIN(13) gives 1101. Add places to pad with zeros, e.g. =DEC2BIN(5,8) gives 00000101.

25=BIN2DEC(1101)

BIN2DEC changes a binary number into its decimal value. =BIN2DEC(1101) gives 13. Use it to check a hand conversion.

26transistor

A tiny electronic switch that is either off (0) or on (1), so it holds exactly one bit. Digital hardware joins millions of them to work with data.

27binary reliability

Two states (on or off) are easy to tell apart even when signals are weak or noisy. Ten voltage levels would be easy to confuse, so binary makes errors less likely.

28two physical states

Storage keeps each bit as one of two physical conditions, such as charged or not charged, magnetised one way or the other, or a pit or a flat area. One condition is 0 and the other is 1.

29logic gate

An electronic component that takes one or two binary inputs (0 or 1) and gives one binary output (0 or 1) by a fixed rule. Processors are built from many gates.

30Computers use binary because their hardware has two states

A clear explanation says digital hardware has two states (on and off), so it stores numbers as 0s and 1s, and it gives the reason using the word because.