prefix of 10^3

Each item in a store's inventory is assigned a unique binary sequence using binary numerals. If the shop has between 75 and 100 goods in its inventory, what is the minimum amount of bits necessary for each binary sequence?

ʙᴇʟᴏᴡ ɪꜱ ʜᴏᴡ ᴛʜᴇ ꜰɪʟᴇɴᴀᴍᴇꜱ ᴀʀᴇ ʀᴇᴘʀᴇꜱᴇɴᴛᴇᴅᴀʀʀᴀʏ[] = [50, 11, 33, 21, 40, 50, 40, 40, 21]ʙᴇʟᴏᴡ ɪꜱ ᴛʜᴇ ᴇxᴘᴇᴄᴛᴇᴅ ᴏᴜᴛᴘᴜᴛ ᴀꜰᴛᴇʀ ᴅᴇ-ᴅᴜᴘʟɪᴄᴀᴛɪᴏɴᴀʀʀᴀʏ[] = [11, 21, 33, 40, 50] ʏᴏᴜ ᴄᴀɴɴᴏᴛ ᴜꜱᴇ ʟɪʙʀᴀʀʏ ꜰᴜɴᴄᴛɪᴏɴꜱ ᴛᴏ ᴇɪᴛʜᴇʀꜱᴏʀᴛ ᴀɴᴅ ᴏʀ ᴘᴇʀꜰᴏʀᴍ ᴛʜᴇ ᴅᴇ-ᴅᴜᴘʟɪᴄᴀᴛɪᴏɴ ᴏᴘᴇʀᴀᴛɪᴏɴ. ɪɴ ᴊᴀᴠᴀ ɪᴍᴘʟᴇᴍᴇɴᴛ ᴛʜᴇ ꜰᴜɴᴄᴛɪᴏɴ ɪɴ ꜱᴜᴄʜ ᴀ ᴡᴀʏ ᴛʜᴀᴛ ʏᴏᴜʀ ꜱᴏʟᴜᴛɪᴏɴ ꜱᴏʟᴠᴇꜱᴛʜᴇ ᴘʀᴏʙʟᴇᴍ ᴡɪᴛʜ ᴏ(ɴ ʟᴏɢ2(ɴ)) ᴛɪᴍᴇ ᴄᴏᴍᴘʟᴇxɪᴛʏ ᴏᴠᴇʀᴀʟʟ ʙᴜᴛ ꜱᴛᴀʏꜱ ᴡɪᴛʜɪɴ ᴛʜᴇ ʙᴏᴜɴᴅꜱ ᴏꜰ ᴏ(1) ꜱᴘᴀᴄᴇ ᴄᴏᴍᴘʟᴇxɪᴛʏ. ʜᴇʀᴇ, ɴ ɪꜱ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴛʜᴇ ʟɪꜱᴛ ᴏꜰɪɴᴘᴜᴛ ɪɴᴛᴇɢᴇʀꜱ (ᴀʀʀᴀʏ). ɪ ʙᴇʟɪᴇᴠᴇ ᴛʜᴇ ꜱᴏʀᴛɪɴɢ ʀᴏᴜᴛɪɴᴇ ᴛʜᴀᴛ ᴄᴀɴ ʙᴇ ᴜꜱᴇᴅ ʜᴇʀᴇ ɪꜱ Qᴜɪᴄᴋ ꜱᴏʀᴛ. ᴘʟᴇᴀꜱᴇ ꜱᴛᴀᴛᴇ ᴀꜱ ᴄᴏᴅᴇ ᴄᴏᴍᴍᴇɴᴛ ᴡʜɪᴄʜ ꜱᴏʀᴛɪɴɢ ʀᴏᴜᴛɪɴᴇ ʏᴏᴜ ᴀʀᴇ ᴜꜱɪɴɢ, ꜱᴏʀᴛ ᴛʜᴇ ᴀʀʀᴀʏ ᴡɪᴛʜ ᴛʜᴀᴛ ᴀʟɢᴏʀɪᴛʜᴍ ᴀɴᴅ ꜱᴏʟᴠᴇ ᴛʜᴇ ᴅᴇ-ᴅᴜᴘʟɪᴄᴀᴛɪᴏɴ ᴘʀᴏʙʟᴇᴍ ᴛʜᴇʀᴇᴀꜰᴛᴇʀ. ᴅᴇ-ᴅᴜᴘʟɪᴄᴀᴛɪᴏɴ ᴘᴀʀᴛ ᴏꜰ ᴛʜᴇ ꜱᴏʟᴜᴛɪᴏɴ ɪɴ ɪᴛꜱᴇʟꜰ ᴍᴜꜱᴛ ᴀᴅʜᴇʀᴇ ᴛᴏ ᴏ(ɴ) ᴛɪᴍᴇ ᴀɴᴅ ᴏ(1) ꜱᴘᴀᴄᴇ ʙᴏᴜɴᴅꜱ ᴄᴏᴍᴍᴇɴᴛ ᴇᴠᴇʀʏ ʟɪɴᴇ ᴏꜰ ᴄᴏᴅᴇᴘʟᴇᴀꜱᴇ ᴡʀɪᴛᴇ ᴛᴇꜱᴛ-ᴄᴀꜱᴇꜱ ᴏɴ ʜᴏᴡ ᴏɴᴇ ᴡᴏᴜʟᴅᴛᴇꜱᴛ ᴛʜᴇ ꜱᴏʟᴜᴛɪᴏɴ ᴀꜱꜱᴜᴍᴘᴛɪᴏɴꜱ ᴀɴᴅ ʜᴇɴᴄᴇ ᴛʜᴇ ᴄᴏᴅᴇ ᴇxᴀᴍᴘʟᴇ ᴏꜰ ᴄᴀꜱᴇꜱ ᴛᴏ ʙᴇ ᴛᴇꜱᴛᴇᴅ ꜰᴏʀ ᴀʀᴇ ʟɪᴋᴇ : ᴡʜᴀᴛ ɪꜰ ᴛʜᴇ ᴀʀʀᴀʏ ɪɴᴘᴜᴛ ᴡʜɪᴄʜɪꜱ…

Compute the following modular exponents.5^5mod13 = 7^9mod8 = 9^10mod11 =

A store uses binary numbers to assign a unique binary sequence to each item in its inventory. What is the mimimum number of bits required for each binary sequence if the store has between 75 and 100 items in its inventory?

Consider the following segment table:Segment   Base   Length0                219     6001                2300   142                90       1003                1327    5804                1952    96What are the physical addresses for the following logical addresses?     segment #    limita. 0                  430b. 1                  10c. 2                  500d. 3,                400e. 4                 112

ʙᴇʟᴏᴡ ɪꜱ ʜᴏᴡ ᴛʜᴇ ꜰɪʟᴇɴᴀᴍᴇꜱ ᴀʀᴇ ʀᴇᴘʀᴇꜱᴇɴᴛᴇᴅᴀʀʀᴀʏ[] = [50, 11, 33, 21, 40, 50, 40, 40, 21]ʙᴇʟᴏᴡ ɪꜱ ᴛʜᴇ ᴇxᴘᴇᴄᴛᴇᴅ ᴏᴜᴛᴘᴜᴛ ᴀꜰᴛᴇʀ ᴅᴇ-ᴅᴜᴘʟɪᴄᴀᴛɪᴏɴᴀʀʀᴀʏ[] = [11, 21, 33, 40, 50] ʏᴏᴜ ᴄᴀɴɴᴏᴛ ᴜꜱᴇ ʟɪʙʀᴀʀʏ ꜰᴜɴᴄᴛɪᴏɴꜱ ᴛᴏ ᴇɪᴛʜᴇʀꜱᴏʀᴛ ᴀɴᴅ ᴏʀ ᴘᴇʀꜰᴏʀᴍ ᴛʜᴇ ᴅᴇ-ᴅᴜᴘʟɪᴄᴀᴛɪᴏɴ ᴏᴘᴇʀᴀᴛɪᴏɴ. ɪɴ ᴊᴀᴠᴀ ɪᴍᴘʟᴇᴍᴇɴᴛ ᴛʜᴇ ꜰᴜɴᴄᴛɪᴏɴ ɪɴ ꜱᴜᴄʜ ᴀ ᴡᴀʏ ᴛʜᴀᴛ ʏᴏᴜʀ ꜱᴏʟᴜᴛɪᴏɴ ꜱᴏʟᴠᴇꜱᴛʜᴇ ᴘʀᴏʙʟᴇᴍ ᴡɪᴛʜ ᴏ(ɴ ʟᴏɢ2(ɴ)) ᴛɪᴍᴇ ᴄᴏᴍᴘʟᴇxɪᴛʏ ᴏᴠᴇʀᴀʟʟ ʙᴜᴛ ꜱᴛᴀʏꜱ ᴡɪᴛʜɪɴ ᴛʜᴇ ʙᴏᴜɴᴅꜱ ᴏꜰ ᴏ(1) ꜱᴘᴀᴄᴇ ᴄᴏᴍᴘʟᴇxɪᴛʏ. ʜᴇʀᴇ, ɴ ɪꜱ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴛʜᴇ ʟɪꜱᴛ ᴏꜰɪɴᴘᴜᴛ ɪɴᴛᴇɢᴇʀꜱ (ᴀʀʀᴀʏ). ɪ ʙᴇʟɪᴇᴠᴇ ᴛʜᴇ ꜱᴏʀᴛɪɴɢ ʀᴏᴜᴛɪɴᴇ ᴛʜᴀᴛ ᴄᴀɴ ʙᴇ ᴜꜱᴇᴅ ʜᴇʀᴇ ɪꜱ Qᴜɪᴄᴋ ꜱᴏʀᴛ. ᴘʟᴇᴀꜱᴇ ꜱᴛᴀᴛᴇ ᴀꜱ ᴄᴏᴅᴇ ᴄᴏᴍᴍᴇɴᴛ ᴡʜɪᴄʜ ꜱᴏʀᴛɪɴɢ ʀᴏᴜᴛɪɴᴇ ʏᴏᴜ ᴀʀᴇ ᴜꜱɪɴɢ, ꜱᴏʀᴛ ᴛʜᴇ ᴀʀʀᴀʏ ᴡɪᴛʜ ᴛʜᴀᴛ ᴀʟɢᴏʀɪᴛʜᴍ ᴀɴᴅ ꜱᴏʟᴠᴇ ᴛʜᴇ ᴅᴇ-ᴅᴜᴘʟɪᴄᴀᴛɪᴏɴ ᴘʀᴏʙʟᴇᴍ ᴛʜᴇʀᴇᴀꜰᴛᴇʀ. ᴅᴇ-ᴅᴜᴘʟɪᴄᴀᴛɪᴏɴ ᴘᴀʀᴛ ᴏꜰ ᴛʜᴇ ꜱᴏʟᴜᴛɪᴏɴ ɪɴ ɪᴛꜱᴇʟꜰ ᴍᴜꜱᴛ ᴀᴅʜᴇʀᴇ ᴛᴏ ᴏ(ɴ) ᴛɪᴍᴇ ᴀɴᴅ ᴏ(1) ꜱᴘᴀᴄᴇ ʙᴏᴜɴᴅꜱ ᴄᴏᴍᴍᴇɴᴛ ᴇᴠᴇʀʏ ʟɪɴᴇ ᴏꜰ ᴄᴏᴅᴇᴘʟᴇᴀꜱᴇ ᴡʀɪᴛᴇ ᴛᴇꜱᴛ-ᴄᴀꜱᴇꜱ ᴏɴ ʜᴏᴡ ᴏɴᴇ ᴡᴏᴜʟᴅᴛᴇꜱᴛ ᴛʜᴇ ꜱᴏʟᴜᴛɪᴏɴ ᴀꜱꜱᴜᴍᴘᴛɪᴏɴꜱ ᴀɴᴅ ʜᴇɴᴄᴇ ᴛʜᴇ ᴄᴏᴅᴇ ᴇxᴀᴍᴘʟᴇ ᴏꜰ ᴄᴀꜱᴇꜱ ᴛᴏ ʙᴇ ᴛᴇꜱᴛᴇᴅ ꜰᴏʀ ᴀʀᴇ ʟɪᴋᴇ : ᴡʜᴀᴛ ɪꜰ ᴛʜᴇ ᴀʀʀᴀʏ ɪɴᴘᴜᴛ ᴡʜɪᴄʜɪꜱ…

(nn+n2n+5n)(n!+2n)  Estimate big oh