Question

Divide 0001010001001001 (BCD) by (1001)2 and express the result in octal equivalent .

Answer 1

Answer on Question #45916, Programming, Other

Divide 0001010001001001 (BCD) by (1001)2 and express the result in octal equivalent.

Binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight

In this case every four bits represents one decimal digit

$$0001\ 0100\ 0100\ 1001\ (BCD) = 1449_{10}$$

Each digit of the binary number is $2^n$ in decimal

$$1001_2 = 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 = 9_{10}$$ $$\frac{0001\ 0100\ 0100\ 1001\ (BCD)}{1001_2} = \frac{1449_{10}}{9_{10}} = 161_{10}$$

For binary - octal translation we may use series of divisions by 8 :

Take remainder of the division by 8, it will be smallest octal digit.

$$\left\lfloor \frac{161}{8} \right\rfloor = 1$$

Then work with integer part of division by 8, as with input number, and do the same operation's till it become zero

$$\left\lfloor \frac{161}{8} \right\rfloor = 20$$ $$\left\lfloor \frac{20}{8} \right\rfloor = 4$$ $$\left\lfloor \frac{16}{8} \right\rfloor = 2$$ $$\left\lfloor \frac{2}{8} \right\rfloor = 2$$ $$\left\lfloor \frac{2}{8} \right\rfloor = 0$$

The end of cycle

And we get :

$$161_{10} = 241_8$$

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