1. Examples
1. (1011001)2 = ( ? )Excess 3
Solution:
(1011001)2 = (_______)XS3
1. Convert binary to decimal
(1011001)2 = (_______)10
`1011001`
` = 1 × 2^6 + 0 × 2^5 + 1 × 2^4 + 1 × 2^3 + 0 × 2^2 + 0 × 2^1 + 1 × 2^0`
`= 1 × 64 + 0 × 32 + 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1`
`= 89`
`:.` (1011001)2 = (89)10
2. Convert decimal to XS3
(89)10 = (_______)XS3
`:.` (89)10 = (10111100)XS3
`:.` (1011001)2 = (10111100)XS3
2. (101100111)2 = ( ? )Excess 3
Solution:
(101100111)2 = (_______)XS3
1. Convert binary to decimal
(101100111)2 = (_______)10
`101100111`
` = 1 × 2^8 + 0 × 2^7 + 1 × 2^6 + 1 × 2^5 + 0 × 2^4 + 0 × 2^3 + 1 × 2^2 + 1 × 2^1 + 1 × 2^0`
`= 1 × 256 + 0 × 128 + 1 × 64 + 1 × 32 + 0 × 16 + 0 × 8 + 1 × 4 + 1 × 2 + 1 × 1`
`= 359`
`:.` (101100111)2 = (359)10
2. Convert decimal to XS3
(359)10 = (_______)XS3
3
+3
=6 | 5
+3
=8 | 9
+3
=12 | | 0110 | 1000 | 1100 |
`:.` (359)10 = (011010001100)XS3
`:.` (101100111)2 = (011010001100)XS3
This material is intended as a summary. Use your textbook for detail explanation.
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