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Binary Integers

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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
...read more.

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
...read more.

Conclusion

Binary integer

Denary

27

26

25

24

23

22

21

1

1

1

0

0

1

1

0

1

205

Denary integer

  • Start on your left.
  • 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.

...read more.

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