Binary Vs Denary
By DarthVader
Date: 2025-01-04
Topic: 223 see comments
Post views: 87
Denary system:
Denary Number Example: 11,111 (Eleven thousand One hundred and Eleven)
Weighting | Ten Thousand (104) | Thousands (103) | Hundreds (102) | Tens (101) | Units (100) |
Denary Number | 1 | 1 | 1 | 1 | 1 |
Binary system:
Binary Number Example: 11,111 (Eleven thousand One hundred and Eleven)
n × 213 | n × 212 | n × 211 | n × 210 | n × 29 | n × 28 | n × 27 | n × 26 | n × 25 | n × 24 | n × 23 | n × 22 | n × 21 | n × 20 |
8192 | 4096 | 2048 | 1024 | 512 | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |
So:
11,111 = 0010 1011 0110 0111
Hexadecimal system:
Hex Number Example: 11,111 (Eleven thousand One hundred and Eleven)
Weighting | 164 | 163 | 162 | 161 | 160 |
Value | 65536 | 4096 | 256 | 16 | 1 |
2 | B (B = 11) | 6 | 7 | ||
2(4096) | 11(256) | 6(16) | 7(1) |
So:
11,111 = 0010 1011 0110 0111 = 2B67
Binary | Denary | Hex |
0000 | 0 | 0 |
0001 | 1 | 1 |
0010 | 2 | 2 |
0011 | 3 | 3 |
0100 | 4 | 4 |
0101 | 5 | 5 |
0110 | 6 | 6 |
0111 | 7 | 7 |
1000 | 8 | 8 |
1001 | 9 | 9 |
1010 | 10 | A |
1011 | 11 | B |
1100 | 12 | C |
1101 | 13 | D |
1110 | 14 | E |
1111 | 15 | F |
Binary coded decimal (BCD) system:
BCD Number Example: 11,111 (Eleven thousand One hundred and Eleven)
Each digit is represented by its binary code equivalent so:
0001 0001 0001 0001 0001 = 11,111
2's Complement (Negative 8 bit binary):
In 2's complement , the first bit of an 8 bit binary number is -128, so:
27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 |
-128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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