Complete the chart by converting the given number to each of the other number sy

Question

Complete the chart by converting the given number to each of the other number systems Complete the chart by converting the given number to each of the other number. Use hexadecimal numbers for sign magnitude, I's complement, and 2 complement. Determine the decimal values of the following single-precision floating-point numbers: 0 10000100 10000100000000000000000 Perform each arithmetic operation in the 2's complement form: 11011001 + 11100111 01100101-11101000 Simplify as much as possible ABC[AB + bar C(BC + AC)] bar x bar y + bar x + y

Explanation / Answer

There are multiple questions in this. Please post separate question for the part 2 and one question for 3,4,5. I will answer the first 1 with their subparts.

1)

Octal 76

We know that octal has a base 8.

So in decimal it will be 7*8 + 6 = 62

In binary it will be we need to divide it by 3 and keep getting the reminder

0011_1110

For hexadecimal we need to divide it in pair of 4 and then use the hexa notation.

So 62 in hexadecimal will be

3E

BCD will be excess 3 code which means in decimal it will be 65 i.e adding 3 to the decimal value.

In binary it will be 0100_0001

b)

Hexadecimal 57.

In decimal it will be 16*5 + 7 = 87

In binary it will be 0101_0111

For octal we need to make pairs of 3 for binary number

001_010_111

so it will be 127 in octal.

BCD will be 87+3 = 90 in binary will be 0101_1010

c)

Binary number is 100101

decimal will be 25 * 1 + 22 *1 + 1 = 32+4+1 = 37

Hexadecimal will be 0010_0101 implies 25

Octal will be 100_101 implies 45

BCD will be 37+3 = 40 in binary will be 0010_1000

d)

Decimal value id 64.

We need to divide it by 2. we know that 2^7 = 64

in binary it will be

0100_0000

in Hexadecimal it will become 40

For octal we need to make pairs of 3 and decode

001_000_000 so it will be 100 in octal

BCD will be 67 in decimal or 0100_0011

e)

we have BCD as 0110_1001

in decimal it will be 105 (1+8+32+64)

we need to subtract 3.

so actual number in decimal is 102.

in decimal it will be 0110_0110

hexa number will be 66

octal will be 146.

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