Write each as a decimal number.- (^100100) two 5. (^101101) two 6. (^111111) two
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page 115 for exercise sets.
Enrichment:
Binary Numbers
Objective To explore place value in the binary system• To convert between
decimal and binary numbers• To relate binary numbers to “on-off” applications
Computers operate at high speed because of the design of
their electronic circuits. You can use binary numbers to
describe “on-off” situations within the computer circuitry.
Place value in the binary system works just as it does in the
decimal system. In the base-10 system, each place is a power
of 10 (that is, 10^0 , 10^1 , 10^2 , and so on.) In the binary system,
each place is a power of 2 (that is, 2^0 , 2^1 , 2^2 , and so on).
- The chart above at the right shows the place values of the
digits in the base-10 number 46. - In the binary system, the same number is written
as 101110two. The chart at the right shows the place
value of each digit in this number.
Convert a Binary Number to a Decimal Number
Convert the binary number 101110twoto decimal form.
- Express the number in expanded binary notation and evaluate it.
(^101110) two(1 25 ) (0 24 ) (1 23 ) (1 22 ) (1 21 ) (0 20 )
32 0 8 4 2 0
46
Convert a Decimal Number to a Binary Number
Convert 46 to binary form.
46
103 102 101 100
thousandshundredstensones
101110
25 24 23 22 21 20
thirty-twossixteenseightsfourstwosones
25 , or 32 32
46
46 32 14
23 , or 8 8
14
14 8 6
22 , or 4 4
6
6 4 2
21 , or 2 2
2
2 2 0
101110
25
(32)
24
(16)
23
(8)
22
(4)
21
(2)
20
(1)
Find the greatest power of 2 that is less than or equal
to the number. Subtract that power from the number.
Find the greatest power of 2 that is less than or equal
to the difference and subtract that from the difference.
Continue until the difference is 0.
Make a chart. Write 1s in the places for all the powers
of 2 you subtracted. Write 0s in the other places.
So 46 in the base-10 system is 101110twoin the binary system.
Write each as a binary number.
- 93 2. 81 3. 64
7.Discuss and Write Compare the binary and decimal place-value systems.