The cerebral hemisphere is each half of the brain responsible for specific functions, and the cerebral cortex is essential for higher neurological functions.
Cerebral hemisphere, one half of the bilaterally symmetrical cerebrum, is the term used to describe each of the two halves of the brain. These hemispheres carry out various functions, with the right hemisphere controlling functions on the left side of the body and vice versa. The cerebral cortex is the outermost part of the brain, made up of two hemispheres separated by a large sulcus, and responsible for higher neurological functions.
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