Question

Convert from twos compliment in 7 bits to base ten (decimal)

a. 1100010

b. 0101010

Answer 1

Please go through the solution given below.If find any difficulty,feel free to ask in comment section.Please do upvote the answer.Thank you.

Converting 2's complement binary to decimal form procedure

• Check the left most digit of the number which represent the sign
• If it is 0, then the number is positive and if it is 1,then the number is negative
• If the number is positive,simply convert it into decimal.This is done by sum up the product of each bit and their weight(2⁰,2¹,2²,....)
• If the number is negative make it positive by inverting the bits,all 0's to 1's and all 1's to 0's and add 1 to it.
• Then convert the result obtained to decimal.
• The negative of this decimal number is the decimal form of the original binary number

a)1100010

• The left most digit of the number is 1.So the number is negative
• Invert all bits and add 1
• 0011101+1 =0011110
• Convert 0011110 to decimal
• 0011110 = 1x2⁴+1x2³+1x2^{2​​​​​}+1x2¹+0x2⁰ = 16+8+4+2+0= 30
• So the decimal equivalent of 1100010 is -30

b)0101010

• The left most digit of the number is 0.So the number is positive
• Convert 0101010 to decimal
• 0101010 =1x2⁵+ 0x2⁴+1x2³+0x2^{2​​​​​}+1x2¹+0x2⁰ = 32+0+8+0+2=42
• So the decimal equivalent of 0101010 is 42