BCD 0001 0010 0011 → pure binary
exam standardthe conversion that needs real arithmetic
Answer
1111011
Why this example is worth doing
Converting BCD to a pure binary integer is not regrouping — it requires multiplying by ten and adding, digit by digit, because the two representations have genuinely different place values. The page contrasts it with the hex-to-binary conversion on the base converter page, which is pure grouping, and the comparison explains why: sixteen is a power of two and ten is not.
Try your own input in the BCD converter. Pack and unpack binary-coded decimal, and add with the +6 correction shown.
How the answer is reached
Decode packed BCD 000100100011
| group | bits | digit |
|---|---|---|
| 0 | 0001 | 1 |
| 1 | 0010 | 2 |
| 2 | 0011 | 3 |
value123
Base 10 to base 2
Convert 123 from base 10 to base 2. The sign is carried across unchanged; only the magnitude is converted.
| digit | value | weight | weight (base 10) | digit x weight |
|---|---|---|---|---|
| 1 | 1 | 10^2 | 100 | 100 |
| 2 | 2 | 10^1 | 10 | 20 |
| 3 | 3 | 10^0 | 1 | 3 |
| total | 123 |
Integer part: divide by 2 and read the remainders bottom to top.
| n | divide by | quotient | remainder |
|---|---|---|---|
| 123 | 123 ÷ 2 | 61 | 1 |
| 61 | 61 ÷ 2 | 30 | 1 |
| 30 | 30 ÷ 2 | 15 | 0 |
| 15 | 15 ÷ 2 | 7 | 1 |
| 7 | 7 ÷ 2 | 3 | 1 |
| 3 | 3 ÷ 2 | 1 | 1 |
| 1 | 1 ÷ 2 | 0 | 1 |
123 (base 10)1111011 (base 2)