written 6.9 years ago by | modified 22 months ago by |

**Mumbai University > Electronics and Telecommunication Engineering > Sem 3 > Digital Electronics**

**Marks:** 5M

**Year:** May 2016

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Write $(AB)_{16}$ into its BCD code and octal code.

written 6.9 years ago by | modified 22 months ago by |

**Mumbai University > Electronics and Telecommunication Engineering > Sem 3 > Digital Electronics**

**Marks:** 5M

**Year:** May 2016

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written 6.9 years ago by |

**i) Conversion to BCD:**

The hexadecimal number is $(AB)_{16}$

**First convert it into decimal number:**
$(AB)_{16}$ = $10 \times {16^1}$ + $11 \times {16^0}$ $ = 160 + 11 = 171 = {(171)_{10}}$

BCD code for ${(171)_{10}}$ is 0001 0111 0001

Combine all binary bits by removing spaces, 000101110001

Hence ${(AB)_{16}} = {(000101110001)_{BCD}}$

**ii) Conversion to Octal code:**

The conversion takes place as follows

**Covert ${(AB)_{16}}$ into binary:**

**Combine 4 – bit binary sections by removing spaces:**

${(AB)_{16}} = {(10101011)_2}$

**Group these binary bits into group of 3 – bits:**

Each 3 bit group is converted to an octal digit

Thus ${(AB)_{16}} = {(253)_8}$

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