Question

pls ignore 1 and 2

12 bit register (signed) int Show" Our Work 1. Qty? 2. range 3. Store Fl: 97. F2:- 326 Fl + F2:7 6. Convert dts from # #5 to octal to hex 7. to decina / 8 5.

The problem lists the decimal value, but registers store binary numbers so you will need to convert them to binary

You will also need to do the 2's complement method on the negative value.

thank you

Answer 1

step3: F1: (000001100001)₂ // In 2's cpmplement // (97)₁₀

step4: F2: (111010111010)₂ // In 2's cpmplement // (-326)₁₀

step5: F1 + F2 // addtion

F1: (0 0 0 0 0 1 1 0 0 0 0 1)₂
F2: (1 1 1 0 1 0 1 1 1 0 1 0)₂
---------------------------------------
(1 1 1 1 0 0 0 1 1 0 1 1 )₂

(111100011011)₂ // Result in  2's cpmplement

((-1) × 2¹¹) +(1 × 2¹⁰)+(1 × 2⁹)+(1 × 2⁸)+(0 × 2⁷)+(0 × 2⁶)+(0 × 2⁵)+(1 × 2⁴) +(1 × 2³)+(0 × 2²)+(1 × 2¹)+(1 × 2⁰)

-2048+1024+512+256+0+0+0+16+8+0+2+1

-2048+1819

-229

step6: convert into octal  

(111100011011)₂

(111 100 011 011)₂ // make group of 3 bits for octal

(7 4 3 3)₈

step7: convert into Hexadecimal

(111100011011)₂

(1111 0001 1011)₂ // make group of 4 bits for hexadecimal

(7 1 B )16

step8: convert into decimal

(111100011011)₂ // Result in  2's cpmplement

((-1) × 2¹¹) +(1 × 2¹⁰)+(1 × 2⁹)+(1 × 2⁸)+(0 × 2⁷)+(0 × 2⁶)+(0 × 2⁵)+(1 × 2⁴) +(1 × 2³)+(0 × 2²)+(1 × 2¹)+(1 × 2⁰)

-2048+1024+512+256+0+0+0+16+8+0+2+1

-2048+1819

-229 // decimal

Note:

• Binary number always stored in computer in 2's cpmplement format.
• we can store the final result into 12 bit Register (sign magnitute format)
• (1 00011100101)₂
• 12 bit Register (sign magnitute format) // First bit indicate sign and remaining bit indicate magnitute

Register = (1 00011100101)₂ // -229