Binary Conversion
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The document provides information about binary number systems and how to convert between binary and decimal numbers. It explains that binary represents numbers using only two digits, 0 and 1, and that each digit represents a place value that is a power of two. It then gives examples of how to convert specific decimal numbers, like 98 and 21, into their binary equivalents by repeatedly dividing by two and recording the remainders. The reverse process of converting binary numbers to decimal, like converting 11101, is also demonstrated through repeated multiplication and addition.
Binary Conversion
- 1. B nar y i In 1854, British mathematician George Boole published a paper detailing a system of logic that would become known as Boolean algebra. His logical system proved instrumental in the development of the binary system, particularly in its implementation in electronic circuitry.
- 2. B nar y i A numbering systems that only uses two digits. 0 and 1. Rather than a base ten that we are all familiar with. Computers use binary to store information in a digital format. Each digit ( 0 or 1) represents one bit Eight bits are equal to one byte.
- 3. Bt i One Binary Digit abbreviation is “b” Can be thought of as one character Either a 1 or a 0
- 4. B e yt Eight bits make up one byte Abbreviation “B” Combination of 1’s and 0’s Can be thought of as one character 11101010
- 5. ki l obi t 1024 bits Abbreviation “Kb”
- 6. ki l obyt es Represented by KB Slang “Kilo” Is equal to 1024 bytes 210
- 7. megabyt es Represented by MB Slang “Meg” Is equal to 1,000000 bytes One million bytes 220
- 8. gi gabyt e Represented by GB Slang “Gig” Equal to 1,000,000,000 Bytes One Billion bytes 230
- 9. t er abyt e Represented by TB Slang “tera” Equal to 1,000,000,000,000 Bytes One Trillion bytes 240
- 10. pet abyt e Represented by PB Slang “peta” Equal to 1,000,000,000,000,000 Bytes One Thousand Trillion bytes 250
- 11. exabyt e Represented by EB Slang “exa” Equal to 1,000,000,000,000,000,000 Bytes One Million Trillion bytes 260 All printed materialin the world would use about 5 Exabytes
- 12. Think of Binary as light bulbs that are either ON or Off
- 13. One Light bulb represents one Bit All eight of these Light bulbs would represent one byte
- 14. 1 0 0 0 0 0 0 1 Think of Binary as light bulbs that are either ON or Off
- 15. B nar y Exer ci se i Binary Exercise Bit Postion Bit 8 Bit 7 Bit 6 Bit 5 Bit 4 Bit 3 Bit 2 Bit 1 Total Binary Value Position Value 128 64 32 16 8 4 2 1 255 if ON Position Value 0 0 0 0 0 0 0 0 0 if OFF Turn a Postion 1 0 0 0 0 0 0 1 ON Here we would ADD The Postion Value Here we bring The Postion Value 128 1 129 DOWN In this incidence our binary Number 10000001 would have a value of 129 Because Postion 8 is ON Postion 7 is OFF Postion 6 is OFF Position 5 is OFF Position 4 is Off Postion 3 is OFF Postion 2 is OFF and Position 1 is ON.
- 16. B nar y i Figuring Binary. Starting on the right going to the left The first digit will be 1 The second digit will be 2 The third digit will be 4 The fourth digit will be 8 The fifth digit will be 16 The sixth digit will be 32 The seventh digit will be 64 The eighth digit will be 128
- 17. B nar y i Base Ten numbers are tabulated Left to Right.
- 18. B nar y i Binary numbers are tabulated Right to Left.
- 19. Exam e pl 10000000 The 1st – 7th digit would be Off The Eighth digit would be On The first digit will be 1 0 The second digit will be 2 0 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 +128 Add the bits The value of the number would be Total 128
- 20. Exam e pl 10000001 The 1st digit would be On The 2nd – 7th digit would be Off The Eighth digit would be On The first digit will be 1 1 The second digit will be 2 0 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 +128 Add the bits The value of the number would be Total 129
- 21. Exam e pl 10000011 The 1st digit would be On The 2nd digit would be On The 3rd – 7th digit would be Off The Eighth digit would be On The first digit will be 1 1 The second digit will be 2 2 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 +128 Add the bits The value of the number would be Total 131
- 22. Exam e pl 10000111 The 1st- 3rd digit would be On The 4th – 7th digit would be Off The Eighth digit would be On The first digit will be 1 1 The second digit will be 2 2 The third digit will be 4 4 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 +128 Add the bits The value of the number would be Total 135
- 23. Exam e pl 11000000 The 1st- 6th digit would be Off The 7th digit would be On The 8th digit would be On The first digit will be 1 0 The second digit will be 2 0 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 64 The eighth digit will be 128 +128 Add the bits The value of the number would be Total 192
- 24. 192 What is the value? 1 1 0 0 0 0 0 0 Think of Binary as light bulbs that are either ON or Off
- 25. Exam e pl 11111111 The 1st- 8th digit would be On The first digit will be 1 1 The second digit will be 2 2 The third digit will be 4 4 The fourth digit will be 8 8 The fifth digit will be 16 16 The sixth digit will be 32 32 The seventh digit will be 64 64 The eighth digit will be 128 +128 Add the bits The value of the number would be Total 255
- 26. 255 What is the value? 1 1 1 1 1 1 1 1 128 64 32 16 8 4 2 1 Think of Binary as light bulbs that are either ON or Off
- 27. U ng C cul at or si al t o f i gur e B nar y N ber s i um First we would open Calculator Start/All Programs/Accessories/Calculator From the Calculator go to View and down To SCIENTIFIC
- 28. Scientific
- 30. This is the Scientific Calculator The next thing we would need to do in select BIN for Binary
- 32. Next we would enter the Binary number For example 10000000
- 34. After entering the Binary number we would then select the Dec Radio Button
- 36. We now see the answer to the problem Is 128
- 38. 192 What is the value? 1 1 0 0 0 0 0 0 Think of Binary as light bulbs that are either ON or Off
- 39. ICT 1
- 40. Deci m t o B nar y al i It follows a starightforward method. It involves dividing the number to be converted, say N by 2 (since binary is in base 2) until we reach the division of (1/2), also making note of all remainders.
- 41. Exam e 1: C pl onver t 98 f r om deci m t o bi nar y al Divide 98 by 2, make note of all the remainder. Continue dividingquotientsby 2, making notes of the remainder. Also, note the star beside the last remainder.
- 42. Division Remainder, R 98/2 = 49 R=0 49/2 = 24 R=1 24/2 = 12 R=0 12/2 = 6 R=0 6/2 = 3 R=0 3/2 = 1 R=1 1/2 = 0 R=1 The sequance of remainders going up gives the answer. Starting from 1*, we have 1100010. Therefore, 98 in decimals is 1100010 in binary
- 43. Exam e 2: C pl onver t 21 i nt o bi nar y Division Remainder, R 21/2 = 10 R=1 10/2 = 5 R=0 5/2 = 2 R=1 2/2 = 1 R=0 1/2 = 0 R=1 Therefore, 21 in decimals is 10101 in binary
- 44. B nar y t o deci m i al Conversion follows the same steps as decimal to binary, except in reverse order. We can begin by multiplying 0 x 2 and adding 1. We continue to multiply the numbers in the “results” column by 2, and adding the digits from left to right in our binary numbers.
- 45. Exam e 1: C pl onver t 11101 f r om bi nar y t o deci mal Operations Result 0x2+1 1 1x2+1 3 3x2+1 7 7x2+0 14 14 x 2 + 1 29 Therefore, 11101 in binary is 29 in decimal.