ACARA Digital Technologies Years 7–8 Definitions Worksheet: Binary Number Representation (Modules 189–203)
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Key terms
Write what each term means, in your own words.
1
most significant bit
2
101_2
3
16 8 4 2 1
4
00000101
5
repeated division by 2
6
convert back
7
binary conversion mistake
8
=DEC2BIN(13)
9
=BIN2DEC(1101)
10
binary reliability
Answer Key
ACARA Digital Technologies Years 7–8 · Modules 189–203 · Student wording will vary for definitions
1most 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.
2101_2 — A small 2 after a number shows it is binary (base 2). Say it digit by digit: one zero one. It means five in decimal, not one hundred and one.
316 8 4 2 1 — The five binary place values. Use a 1 to count a place value and a 0 to skip it. Together they make any whole number from 0 to 31 as five bits, so 31 is 11111.
400000101 — 00000101 is the binary number 101 padded with leading zeros to fill 8 bits. Zeros added on the left do not change the value, so it is still 5.
5repeated 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.
6convert 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.
7binary 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.
8=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.
9=BIN2DEC(1101) — BIN2DEC changes a binary number into its decimal value. =BIN2DEC(1101) gives 13. Use it to check a hand conversion.
10binary 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.