Computer Science: An Overview: Global Edition (12th Edition)

some notes for additions in binary notation: 1- If the most significant bit is 1, then it represents the negative decimal number. 2- The most possible largest positive integer can be represented by using 5 bits pattern is 15. 3- The most possible least negative integer can be represented by using 5 bits pattern is, -16. 4- When two values are added, if there is an extra bit generated after the most significant bit, that is the 6’th bit. Then the 6’th bit is considered as carrying bit and needs to be truncated. 5. $\ \ \$• When two positive numbers are added and the result obtained is negative. $\ \ \$• When two negative numbers are added and the result obtained is positive. 6- When you add and subtract binary numbers you will need to be careful when 'carrying' or 'borrowing.' _____________________________________________________ a. 00011 Step $1 :$ leftmost bit is $(0)$ so we convert normally by multiply every bit of the binary representation to the power of two from right to left, start at $\left( 2^{0}\right)$ Step $2 :$ (0 * 16) + (0 * 8) + (0 * 4) + (1 * 2) + (1 * 1) = 0+0+0+2+1= 3 Therefore, $(00011)_{2}=(3)_{10}$ _____________________________________________________ c. 11100 Step $1 :$ leftmost bit is $(1)$ so we know that number sign is negative and we get value as follows: Step $2 :$ flip all the bits in the signed binary (11100) so (11100) converted to (00011) Step $3 :$ add $(1)$ to converted number (00011 + 1) so $(00011)_2 + (1)_2 = (100)_2$ Step $4 :$ convert $(100)_2$ to its equivalent base ten representations, by multiplying every bit of the binary representation to the power of two from right to left, start at $\left( 2^{0}\right)$ (1 * 4) + (0 * 2) + (0 * 1) = 4+0+0= $(-4)_{10}$ Therefore, $(11100)_{2}= (-4)_{10}$ _____________________________________________________ to solve [ b, d, e, f ] do the previous steps :