what decimal number corresponds to the binary number 11111111?

The binary number 11111111 corresponds to the decimal number 255.

How to see this

Each position in a binary number is a power of 2, starting from the right with 202^020.

For 11111111, all eight bits are 1, so you add:

• 1×27=1281\times 2^7=1281×27=128
• 1×26=641\times 2^6=641×26=64
• 1×25=321\times 2^5=321×25=32
• 1×24=161\times 2^4=161×24=16
• 1×23=81\times 2^3=81×23=8
• 1×22=41\times 2^2=41×22=4
• 1×21=21\times 2^1=21×21=2
• 1×20=11\times 2^0=11×20=1

Adding these: 128+64+32+16+8+4+2+1=255128+64+32+16+8+4+2+1=255128+64+32+16+8+4+2+1=255.

So, the decimal number that corresponds to the binary number 11111111 is 255.