Question

Express the decimal number (-37)10 as an 8-bit 2's complement binary number.

Given the two signed binary numbers (2's comp.) X = -8 and Y = 14, what is their sum?

What is the BCD representation of the decimal value (9371)10?

Answer 1

In 2's Complement Binary Representation we represent signed numbers As signed number are of two types Positive and Negative

1. To represent Positive Numbers we write simply the binary form of that number

2. To represent the Negative Numbers we take 2's Complement of its positive value . For Example - A = ( 2's complement of A )

Here MSB bits decide the sign of the Number

If MSB =1 then Number is Negative

If MSB=0 Then Number is Positive

So We have Decimal Number

-37 = 2's Complement of 37

37 = 11011011

So we get (-37) ₁₀ in  2's complement binary number.= 11011011

Format of Addition of Two Numbers = A - B = A + ( 2's Complement of B )

Here We have

X = -8 and y = 14

S0 14 - 8 = 14 + ( 2's complement of 8 )

14 = 00001110

-8 = 2's complement of 8 = 11111000

Now add them

00001110

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00000110

Now As MSB = 0 so Result is positive and without any overflow

Hence we get Result as = 0000 0110= (6) ₁₀

This is how addition of two signed number is done in 2's Complement method

Convert Decimal To BCD Representation

Firstly, separate the decimal number into its weighted digits and then write down the equivalent 4-bit  BCD code representing each decimal digit

So we have  (9371)₁₀

Separating the digits and writing each 4 bit

9 = 1001

3 = 0011

7 = 0111

1 = 0001

Combine all together we get

BCD Of   (9371)₁₀ = 1001001101110001

This is how we can convert any decimal to BCD

So These are the Complete Solution of all the Questions asked

Thank You

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