Conversion between number system Data view presentation 2 1 variant

Conversion between number system

Learning objectives:

Assesment criteria:
Translates numbers from decimal to binary
Translations of the number of one number system to another

Convert decimal numbers to binary numbers and vice versa

N-based numeration systems

If we take the rule by which numbers are built in the decimal number system, replacing base 10 with a natural number N, we can construct a positional number system with base N.

In computers, a binary number system and related binary - octal and hexadecimal number systems are used.

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Translation of numbers to decimal number system2,8,16 10

When converting a number from a binary (octal, hexadecimal) system to decimal, this number must be represented as the sum of the degrees of the base of its number system.
1)101001102=1*27+0*26+1*25+0*24+0*23+1*22+1*21+0*20=128+32+4+2=16610

2) 7038=7*82+0*81+3*80=448+3=45110

3) 23FA116=2*164+3*163+15*162+10*161+1*160= 131072+12288+3840+160+1=14736110

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Decipher the following facts ...

More than 110010% of people all over the world have never made or received phone calls.

Gorillas sleep about 1110 hours a day.

You can find out the floor by the number of his teeth. Most males have 101000 teeth, females 100100.

Giraffes can brush their ears with a 10101 inch tongue!

A man named Charles Osbourne has been making hiccups for 1000101 years now!

Answers

50
14
40 36
21
69

Translation of numbers from the decimal number system10 2,8,16

Sequentially divide the original number and the resulting quotients by q until we get a quotient, a smaller divisor. The residues obtained from this division — the digits of the number in the q number system — should be written in the reverse order (bottom to top).

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11010

361

14 2 11 = E2B

2

8

16

The game "Who counts more?"

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Translation of numbers from binary number system

To convert a number from binary to octal (hexadecimal), it must be divided into triads (tetrads), starting with the low order (right to left), if necessary, adding the leading triad (tetrad) with zeros and replacing each triad (tetrad) with the corresponding octal (hexadecimal) digit (table).


010 010 110 1112=22678 0100 1011 01112=4В716

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Converting numbers to binary number system

To convert an octal (hexadecimal) number into a binary one, each digit must be replaced by its equivalent binary triad (tetrade).

7268= 111 010 1102
74С16 = 0111 0100 11002
(when writing the number, the first 0 is not written)

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Translation of numbers from the 16th to the 8th and back

FAE16=1111101011102
111 110 101 1102=76568

6358 =1100111012
1 1001 11012=19D16

In the transition from the octal number system to hexadecimal and vice versa, an intermediate translation of numbers into a binary system is necessary.

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