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# Binary Integers

Extracts from this document...

Introduction

Carl Cooper                                                                                                                                    Unit 1

124146                                                                                                                            30/04/2007

Method 1

Binary Integers

• Computer systems use one, two, and three, even four bytes (32 bits) to store a single integer.
 Denary Integer Binary integer 1 00000000 2 00000001 3 00000010 4 00000011 5 1 6 1

Calculating denary integers represented by a binary integer

• Denary integers are worked out by using the unit 10.
 10,000=104 1,000=103 100=102 10=101 1 Denary  integer 4 7 0 9 2 47,092

Binary Integers

• In the same way binary integers can be worked out as numbers based on the number 2.
• Therefore 10010100 represents the denary number 148 and we can write the answer in the table:
 Binary integer Denary 27 26 25 24 23 22 21 1 1 0 0 1 0 1 0 0 148
• 10010100 Binary  =  1x128+0x64+0x32+0x8+1x4+0x2+0x1 Denary

Middle

23

22

21

1

0

0

1

1

1

0

1

0

58

• 00111010 Binary  =  1x32+1x16+1x8+1x2=

= 32+16+8+2

= 58

1. 11101111 =
 Binary integer Denary 27 26 25 24 23 22 21 1 1 1 1 0 1 1 1 1 239
• 11101111 Binary  =  1x128+1x64+1x32+1x8+1x4+1x2+1x1

= 128+64+32+8+4+2+1

= 239

1. 01000011 =
 Binary integer Denary 27 26 25 24 23 22 21 1 0 1 0 0 0 0 1 1 67
• 01000011 Binary  =  1x64+1x2+1x1

Conclusion

 Binary integer Denary 27 26 25 24 23 22 21 1 1 1 0 0 1 1 0 1 205

Denary integer

• Check whether the denary number 205 is greater that the number in the first column 128.
• In this case it is which means that we need 128 in the number, so place 1 in the column.
• 205 – 128 = 77
• 77-64 = 13
• Moving to the next column, check whether 13 is greater that the number in the next column 32.
• As it is not, we place 0 in the column.

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